setting up and verify a wallet under special circumstances A friend of mine has a problem in verifying a wallet for the following reason.

Since about 40 years he has been denied a passport and a normal ID card by the german authorities after he handed in his old IDs after marriage. But it seems there is no chance to set up an BTC wallet that permits usual activities (buying resp. selling and transferring BTC. 

Q: Is there any institution in the EU (using german or english language) that permits wallet on/with alternative identification and is at the same time trustworthy and has high level of integrity?

My friend would intend to buy 3 BTC and following per year one additional BTC for an indefinite period.

I would appreciate someone's help in this matter. Thank you.
It seems your friend is attempting to open an account at an online exchange, this is the general instance in which people new to Bitcoin try to make an initial purchase.

It is important to note that the account they are opening at an online exchange, is not just a bitcoin wallet, but also an exchange trading account. Currently the vast majority of online services do not make proper distinctions or delineations between the difference financial services they offer. 

To create an account and associated set of keys to accept and transfer Bitcoin funds in the Bitcoin blockchain, one does not need to use a service, and may use any number of wallet software options. There are also free online services which do not require any identification to set up and host a wallet using their service.

I will not try to attempt to answer all the security related issues regarding wallet hosting services. This should be a separate area of inquiry for any new user of Bitcoin.

Any market, exchange, or trading platform where users can trade Bitcoin credits for national currencies, is managing transactions in those currencies, and will generally be attempting to comply with local laws respecting those transactions. It is at this point that these services are requiring identification of users, in order to comply with financial regulations.

The common practice of those looking to trade small amounts of Bitcoin credits for national currency, or vice versa, is to find ways to do so in person, rather than online. This usually done by finding someone to meet using an online service like LocalBitcoins.com or meetup.com and then meeting the person, or using a nearby Bitcoin ATM. In either case, small amounts of funds traded between the people or with the ATM are considered to be within legal limits of a non-reportable transaction. You may want to check your local regulations to see what those limits are.

It's good to keep in mind, for those who are new to Bitcoin, that there are two parts to any currency trade you are making for Bitcoin credits. The national currency transfer, and the Bitcoin funds transfer. The national currency transfer is the one that requires identification of users, generally speaking.