Secondly, I have the intention of consolidating all my UTXO's to a single one in my wallet. Normally, I send them to my second wallet to consolidate it and pay a fee in the process. Is it possible to merge them all into a single UTXO in the same wallet?.
Yes you can merge it all into a single utxo using a single transaction and not by just merging it directly in the same address..
I get what you are trying to ask here , it's just this same way you are sending to the other wallet I.e you spend all your UTXO in a single transaction to a new wallet(lets say you did this while the mempoolis less congested)... if the other wallet is an electrum or uses the number of your total inputs for calculation of fee then you've just saved yourself some change from consolidation.
However instead of using a new wallet, You can just use a new address (since electrum supports multiple address), in the process of
consolidation fee is calculated the same way you spend your UTXO to another wallet [ @ hosseinimr93 did mention that]... so you will have to pay even if the transaction is within wallet. After you're done with the consolidation you should have a new INPUT in a different address within the same wallet.
Note: the idea of consolidation is generally for when the mempool is less congested
Also, you can choose to receive UTXO in a new address every time you receive, with that you won't need to worry about consolidation