Of course you can. Addresses don't stop working. Not ever. If you want to use the same address over and over again then by all means do so. Understand that it is bad for your privacy but if you don't care about that then you can do it.
You can see the full list of receiving addresses on the addresses tab which is hidden by default. Go to wallet menu > addresses to bring it into view.
Ok thanks, didn't know this. But that also means I can never give anyone or use myself this Bitcoin address to transfer shares for more than once, right? So I cannot always send BTC to the same address, I always have to look it up before sending to see what's the new address?
No it is not correct. If he wants to he can reuse addresses. It's not good to do so but nothing prevents him from doing so.
Question, if I give my Electrum BTC Adress to someone to send me BTC, after the TX the Adress is changing as you say. What happens if someone sends more BTC to the address before? Will these coins be on this address but I can't get these?
As I've already said above you can continue to use any and all receiving addresses in your wallet as many times as you like. That includes old addresses. Your wallet will watch all those addresses, your wallet balance will reflect transactions involving all those addresses and when you go to spend money it will draw on coins sent to all those addresses.