Why would I trust a cryptocurrency that allow only 3 transactions/s? I noticed that the recent blocks usually includes about 2k transactions with is almost the upper limit (max. 1 MB per block). From this I can see that bitcoin would never allow more than 2000 / 10 * 60 = 3.5 transactions per second which is far below other money services such as PayPal or any credit card company. 

Because the 1 Mb limit is already reached in most blocks (in 2017), I can conclude the bitcoin ecosystem is already fully saturated in terms of transactions per minutes so it cannot expand further more.  

Why should I trust bitcoins and invest my money on it with such considerations? Lots of people believe in bitcoins and put their money on it despite what I mentioned above. 

I know bitcoin is a living ecosystem and the question of increasing the block size to 10 Mb has already emerged. Unfortunately performing any change to such fundamental build block of the system would have an enormous impact on its economy so may be never accepted by the community to make any change to the core code.
You are equating the value of a currency with the performance of just one way to exchange that currency. There are poor ways to exchange dollars as well.

Also, I'm not sure what you mean by "invest in such service". You can invest in bitcoin-related businesses and you can invest in bitcoin, the currency. But I don't see how you can invest in the bitcoin generation and transfer service provided by the blockchain.