Hello Audax, and welcome to the board! Just one unrelated question for you - do you ride brevets?
My answer to this would be "yes, but".
I have felt the presence of God, powerfully at times. Hence the "yes". The "but" comes in as a word of caution - it's very easy to get swayed by feelings and end up seeking the next "spiritual high", that can be unhelpful in many ways. We see the evidence of our Creator all around us so even if we don't feel his presence in a very real tangible sense right now that doesn't mean he isn't there. I like the analogy of the stars - you can't always see them but they are always there.
As for whether prayer works, sometimes it works in ways we can see and immediately associate with a prayer. You might pray for someone to be healed and find their ailment is either treated much more easily than expected, or just goes away completely. You don't have to look very hard to find lots of dramatic third-hand accounts that happened to someone else, in a land far far away, where you have no way of verifying any part of it, but it's a different story entirely when you actually see it for yourself. Sometimes you won't see a very specific answer but will come to accept things the way they are. On other occasions it will be like asking for something and being told "no". (For me the most dramatic example I personally saw was a very dear family friend who was critical in the ICU, not expected to see the end of the week - her husband asked me to call their son to let him know he really needed to get to the hospital and fast. It wasn't much after the end of the week that she walked out of the hospital, alive and well.)
Another analogy to the issue of feeling the presence of Jesus is to think of a walk through the mountains. The experience at the mountaintop is wonderful - the sun is shining brightly and you can see for miles, and get the sense of achievement and awe at being at such a high place. You can see another peak from where you are, but to get to it you have to come down the mountain and walk through the valley to get to it. The valley might be boggy, overgrown, it might be hard going for all sorts of reasons. It might be far enough to the next peak that you have to make an overnight stop in the valley, even if you'd really rather not be there. But then you reach the next peak and the cycle begins.
Sometimes the walk through the valley can last a long time. The crucial thing is to remember God's promises. Jesus said he went to prepare a place for us. He will come for us, just not necessarily for a time.
