Can form entries from a WordPress form go to a database

I am using WordPress 4.3.1.

I have built a stand alone form (form 1) using PHP where one can enter volunteering tasks doable in a city, has fields like volunteering activity, city, state. The values submitted using this form will become data for another form (form 2). Using form 2, someone else who is searching for volunteering tasks can find it. So, if in form 1, I enter, that you can volunteer in Animal Shelter in Atlanta, Georgia it goes to a back-end database. Later, if someone is using form 2 and searches for volunteering activities in Atlanta, Georgia, they should get a result like volunteer in Animal Shelter in Atlanta, Georgia.

I realize form 1’s data can be stored in a back-end database which can be source for form 2 searches.

1. Are there any plug-ins in WordPress which do it? If so, which are they?

2. If not, how can I integrate the two forms built in PHP into the current WordPress theme Salient so that the forms don’t look separate from the website?

3. Are there any frameworks which can speed up the building of form 2?

Thanks