What are the advantages to become a bitcoin node? As far as I understand, the nodes are responsible for verifying the transactions and the blockchain, but also to relay transaction over the bitcoin network. 

Being a bitcoin node require a certain infrastructure and thus it costs money. 

Who wants to create a new bitcoin node and what are the benefits?
There benefit is that you operate a full node in the Bitcoin network. Yes, this is your premise but it's also the consequence of it. You merely seem to not understand what operating a full node means.

If you don't operate a full node, you put trust in others. How much trust you put in others depends on the specifics.

For example, a person who uses a web wallet puts full trust in the operator of that web service. The operators are not only in control of what blockchain is regarded as the effective one but are also in full charge of the user's funds as they hold their private key.

As another example, if you use an SPV client, you don't put as much trust into other. You don't give the privilege of spending (or not spending as you please) your money to a different entity. However, you can be fooled by someone who puts a lot of work into it. That this is going to happen is very unlikely, but it is possible.

Only if you operate a full node, you don't have to trust other entities. You are in full charge of your money. You cannot be fooled by someone sending you an invalid blockchain because you verify everything. You cannot be told that a transaction to you has been confirmed even though it hasn't because you yourself are the authority you get your information about which transactions have and which have not been confirmed.