For your first question...No, you can't just re-boil it. If the lid does not seal, check the jar lip for cracks. If all is well with the jar, wipe down the lip of the jar, get a new lid and re-process the jar.
The second question: yes, when the lid stays pressed. It's sealed, though when it doubt, leave that particular jar in the fridge and use it up first.
SKK is right. The usual reason for a non-seal is a bit of jam on the lip of the jar. A canning funnel helps prevent this, along with careful wiping of the rim and threads with a damp towel before screwing on the lid. And, tempting as it may be, never press on the lid; let it seal by itself. You can always refrigerate a jat that doesn't seal, or even freeze the jam.
To the first part of your question, if when you can your jam a jar doesn't seal take the jam out of the jar and put it in a clean, sterilized jar, with a clean lip. Also put on a new lid under the ring. Check the old jar and see if it has a chip in the lip. Or perhaps it didn't seal because the lip was dirty.
If you're pressing down and the lid is not bouncing back, you've got a good seal. You may have to wait to the jars to cool completely after cooking to have the vacuum action work as well, so be patient!
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The second question: yes, when the lid stays pressed. It's sealed, though when it doubt, leave that particular jar in the fridge and use it up first.