And how to check if the sympathy is mutual? What kind of suggestions should be made?

What to do if you like a person, but you are not sure if she/he likes you back? Here's my proven three-step method:

1. Does the person want to communicate with you? If YES, you like me as a friend and ask the second question. If NO, the person doesn't like you.
2. Does the person want to give you gifts, touch you, or help you with chores? If YES, you like him as a good friend and ask the third question. If NOT, trust him as a friend.
3. Does the person try to kiss you, touch you in interesting places and send you nudes? If YES - you should have already understood at this moment that the sympathy is mutual and the person wants more than friendship. If NOT, you like me as a good friend.

Yes, that's really enough. At least that's what I use.