1. The more invested you are in the music you're playing, the more invested the audience will be. Listeners will engage and connect with you if they sense that what you're doing is important to you. They won't be convinced to engage if they sense that you are more focused on getting them to engage rather than being engaged yourself.
2. If you give people everything up front, they will get bored of listening because there is nothing new, and nothing worth trying to find. However, if you give them a taste up front, and the prompt (musical prompt) that there is more to find with deeper listening and engagement, they will stay focused and interested. They will be enough satisfied with the bit that you gave them, but not too much that they don't search for more. Make sure there IS more to find, otherwise you're toast.
3. You don't have to "entertain" to connect with people. Jumping around the stage and doing somewhat obnoxious musically-suitable physical movements can be cool, but--contrary to popular belief--it's not necessary, and it doesn't necessarily make for a good performer or performance. My all-time favorite performer does little-to-no physical movements (mostly just toe-tapping, if anything), grimaces more than he smiles, and yet conveys the most enjoyment, investment, skill, and "performance-ness" of any player I've ever seen. Please don't misunderstand; I'm not saying you can't entertain, and I'm not saying it's not cool; I'm merely stating that belief in its necessity is incorrect.
4. What the audience *hears* are notes. What they *feel* is tension and release. The way to communicate toward what the audience *feels* is to gain an in-depth understanding of how notes and patterns and other musical aspects you control contribute toward the idea of tension and release. If you only play with notes and don't learn to use them toward an end (that's the whole point of music), the audience will only *hear* your music. But if you learn to use notes toward above-mentioned end, the audience will actually be able to *feel* your music.