Thank you for the answers everybody. I hope someone here can help us to improve our soco’s.

Battery expert here 🖐️ 

Let me answer your questions yetisbey.

1- As a complete noob should I try to my own build or it is better to buy an aftermarket battery?

Difficult question to answer because it changes for each person. Making a battery yourself using individual cells will require some basic tools and even some specialised tools (spot welder comes to mind). 
If you don't have these nor have the possibility of borrowing these tools, they will make you initial investment quite a bit bigger, buying a 2nd aftermarket battery if will not require the purchase of any tools.
Making a battery also takes quite a bit of time and possibly your bike will be in 100 pieces during the process, if your bike is the only means of transportation then perhaps this can cause a big inconvenience.

All these were why you'd want to buy a battery and not make it yourself, but the DIY path is not all doom and gloom. First of all is the pride and joy in building and not buying, second you have the potential money to be earned in the future since building a battery pack can prove to be quite useful as the world is transitioning towards electrical power more and more.
Making e-bikes, repairing car batteries, installing off-grid power walls for domestic use (some of these things will require a license and official training but if you are already familiar with the technology etc, obtaining these required licenses can be easier).

After writing this I guess the short answer should be: will this DIY pack be a one time thing? Yes: don't bother and just buy one. No: invest a bit of tools and you have a possibility of getting a job somewhere or opening your own shop (I got my job because my current boss saw my former DIY e-bike and was impressed, goes to show that this type of knowledge is very useful) 

2-I have found a dealer on Aliexpress he claims that they are selling a BMS which is compatible with the original battery and controller there isn't any need to crack or something (Price is ~80€). Could it be true? Does anyone here have some experience with such third party BMS?

No idea to be honest. In general be very wary of claims made by Aliexpress vendors, they're physically very far away so honestly they don't care about lying.
There is another user here on the forum who had purchased a aftermarket BMS and I believe that his experience was rather good. Try and look for the thread, I believe it was called "built DIY battery and it worked" or something along those lines.

If not then any 17s (17 series) li-ion BMS will work but it won't have the communication with the display to tell how much percentage is left. So think about adding a volt indicator so you can see the SOC (state of charge). Keep in mind that after using the battery for a while you will get a "feel" for when it's time to charge up. 

3- Can I achieve better acceleration only with a BMS or should I replace also the main controller?

Yes and no. The bike will still has less "umpf" as the SOC drops. You, me and everyone else clearly know that with a 100% battery the bike is A LOT more aggressive and twitchy than when it has 20%. This is because the limiting factor of the controller is the amperage (A) and not the voltage (v). The controller allows  a max of 40A of current to go through it.
Power (W) is V*A so:
100% SOC = 71.4v 
Controller limit = 40A
71.4*40=2856W (2.8kW)

Now lets say you run your battery down a bit and your at 54.4v which is pretty darn close to 0%
54.4*40(still the same current limit)=2.1kW.

BIG difference.

On top of that you have a thing called voltage sag but its getting late so I'm wrapping this answer up! 

 Short answer: you can ride longer with a more aggressive but eventually you will using up the battery and will encounter the same "problems".
If you're asking if you will accelerate quicker than you would now with 100% on just the original battery: very slightly because the voltage sag would be less, but honestly don't expect anything big to happen, changing the controller would be necessary for that.

4- The same seller on Aliexpress has also batteries for TC and he told me I can use a 59.5AH (~145km price: 1430$ incl. shipment) battery in parallel with my original battery which lasts ~55km. Can be this true what he says? If yes Is there possibility that too much power damages my TC?

Correct me if I'm wrong but isn't the original battery also 50Ah? My TC is downstairs in the garage so I can't just pop it open and look, but I'm pretty sure it says "60v50Ah" on the top. 
Thus if you get 55km on your original one, placing another same capacity battery will increase it with another 55km, not 145km..  see why I said to not trust Aliexpress vendors*cough cough*.

Placing it in parallel is also not a good idea since your orginal battery already has 1 year of usage. It's capacity isn't 50Ah anymore and thus putting a brand new 50Ah battery in parallel can prove to give issues. 
The difference might not be much and I might be being extra careful here but these big packs are no joke man, if they go AWOL then you could get a nasty fire between your legs.

5- If I try to build a DIY battery, I should get all the necessary tools is it worth investing all of them such as spot welding machine etc.?

Damn it, didn't read this question until know.. I hope my answer to question #1 will suffice for this question too.

-------------end of Q&A cause it's time for bed haha. Hope I clarified a few things. 

Very good answer Bvzijverden, thanks for that. I was actually considering building more than 1 so maybe I will end up investing in a DIY battery with time, maybe in a couple of months.

The original battery is 30Ah, for the largest capacity.

If I got one of these BMS and it turns out they worked, could I potentially build 2 DIY batteries with larger Ah capacity and replace the original one completely?

Say 2x 60v 59.5Ah in parallel or even running separately.

You're very welcome -what good is knowledge if you don't share it with the world :).

To clarify: the tools aren't that expensive it's just when building just 1 battery it seems like a waste of money (even if it's not a lot).
You can make your own spotwelder from an old microwave transformer and some welding cable (I did this since I enjoy the DIY path far more than buying things). 
It works like a charm and creates very solid welds, only downside is that it's not as quick.
After that get a decent soldering iron (~€20 maybe) with some interchangeable tips. At least one big beefy one for soldering on bus bars and a smaller tip one for finer work which might be required. 
I reckon you're looking at €100-€150 investment in terms of tools if you go down the DIY spotwelder route (this will include pretty much everything from your solder to a pair of pliers). 
Looking at it like this, if making more than 1 battery it will be worth your while to make this investment. Needless to say, I enjoy these tools not only for battery making but also for other jobs around the house or paid jobs. 

 Regarding your battery question. 
I wouldn't bother with making 2 small separate batteries, just make 1 big one :).
But there are some situations where you might wants to run 2 smaller batteries in parallel:
Let's say the BMS can deliver only 40A of peak current, having 2 smaller batteries with both their own BMS in parallel will give you a combined 80A of peak current.
Don't worry about this number being higher than the controller since the controller will only "take" as much as it can handle.
The main advantage of having a higher peak current would be for potentially future controller upgrades: 71.4v(100% SOC)*80A=5.7kW.
The original motor will definitely be able to handle 80A but I'm afraid the phase cables of the motor won't. You'd have to open up the motor and replace the smaller cables for some beefier ones that can handle this amount of current.

So that's one advantage of running 2 BMS' in parallel and another one would be that it's more reliable. Say one BMS fails, you still got the other one to get you home. This would never happen because 2 BMS in parallel with the original controller will only draw 20A from each BMS -well below their max rating and thus making it very very unlikely for one to overheat, fail or anything like that.

Now, why then would I still choose a single BMS, larger, battery? Cheaper haha. It saves you the cost of one BMS. I don't know how much this BMS is but every little dime you save can be spend one something else. 
It'd make a 17s25p pack for example and have all the cells connected to one BMS. 
You can of course use the original BMS for this too. Make the whole pack and wait until the last moment to install the BMS to it (this way you minimise the down time of your motor). 

Ps. the original battery is indeed 30Ah, I had a long day when I wrote that original reply 😉