I'm confused what verb is correct.
- Feelings she hardly recognize.
- Feelings she hardly recognizes.
Is the verb 'recognize' for 'she' or for 'feelings'?
Feelings, which are not aware, cognizant beings, can't usually recognize anything. So she must be the subject of the verb.
This is a fairly standard use of the adjective clause, which you should learn to recognize. The typical form is a noun followed by some phrase modifying the noun. Example:
The tree that she used to climb as a child.
It's not uncommon to drop "that" or other subordinate conjunctions from adjective phrases:
The tree (that) she used to climb as a child
The bank teller (who) I spoke with.
The city (which) I grew up in.
And so on. In this case "(that) she hardly recognizes" modifies "feelings". As an example:
Feelings ((that) she hardly recognizes) are rushing over her.
As a side note: It's unusual to hear this sentence in the present tense, as I would expect it to be part of some narrative. Narratives commonly use the past tense:
Feelings she hardly recognized were washing over her.