No, it’s not normal …. but it could be any number of things or a combination .. probably either the action is too low, the truss rod isn’t adjusted correctly or the frets are uneven. It basically sounds like it could do with a good set up, I would take it to a guitar shop (where the people actually know what they are doing) and get it looked at, it shouldn’t cost much and you’ll have an excellent playing guitar afterwards.

maybe the neck just needs a little relief? if you capo at the first fret and then fret at the last fret what’s the gap feel like under the bottom E in the middle of the fretboard? Tap you finger up and down on it and tell me what it’s like, is it a small gap or is there no gap?

it’s really hard to tell without seeing it to be honest… if you close one eye and look down the fretboard do the frets all look parallel with each other? it could be a twist in the neck which is pretty serious or it could just be one or two frets are a little high and just need leveling a bit, check the frets are all seated properly, they might just need tapping in a little more… like I said it’s pretty hard to know what’s going on, you really need to get someone to have a good look at it, a professional should be able to see right away what the problem is… then you can take it from there. If this is a brand new guitar I’d be tempted to take it back to where it came from and ask them to sort it out (or exchange it for another guitar) if that’s possible.

no worries, hope you get it sorted.