#2
1) It's not missing a fret. 21 fret guitars are pretty common (Stratocaster and Telecaster). Very few songs really need the highest frets. Yes, there are solos that need it but you can always play it an octave lower or just play something different. Solos don't need to be covered note for note. Also you could say a 22 fret guitar misses two frets. Or you could say a 24 fret guitar misses six frets. There are guitars with 20, 21, 22, 24 or even 30 frets.

3) No. Scale length doesn't have anything to do with it (unless you have a wrong kind of neck). You can tune your standard guitar to Eb or even something like drop A if you want and the notes will still be in tune. Some guitars just have longer scale length to get more tension for strings (works better for low tunings and you don't have to buy extra thick strings).
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#3
1) Are there songs which I can't play because of the one fret I'm missing?
Not really, MaggaraMarine covered this pretty thoroughly already, although i will point out that there may be some frets that are too squashed together higher up the fretboard for you to be able to fret them comfortably due to the tiny scale length. I have the thinnest fingers ever and even i had some difficulty with those higher frets.

2) I've heard somethings about the guitar going out of tune very easily, is that true?
Not too sure how stable the trem is, but i imagine if that's used sparingly and the guitar is set up properly you should have no such problems.

3) Since its not a full size guitar, are some notes going to be a bit out of tune?
MaggaraMarine also covered this

4) I want flat wounds for it, what gauge should I get? I'm going to play beatles songs mostly.
It's a very, very short scale - 20.5" iirc - so i would honestly recommend 12-52s or higher unless you want really low tension. Bare in mind that flatwounds come with a wound 3rd string which doesn't bend like an unwound 3rd which you might find restricting, and also due to their strong fundamental tone but lack of upper harmonics they can end up sounding a bit undefined and muddy as soon as any overdrive is added. The other awkward thing is, it can be difficult to find string gauges higher than 11-48s that have an unwound 3rd string.

5) Can I get a good beatles tone out of it when I play though a Vox mini 3 set on AC30?
You could get something that's close enough i imagine, but tbh you could also get in that ballpark with a lot of other guitars too.

Honestly, if i were you, i'd save the money and get a 330 or a 625 instead if you really want a rickenbacker - the 325 is a needlessly expensive guitar for people who want to play in beatles tribute bands - it costs twice as much as most other rickenbacker models, but any other rickenbacker model will do everything else much, much better, imo.. And other rickenbacker guitars are pretty good for emulating john lennon's tone anyway. tbh, as long as you get the chord voicings right and remember to pick aggressively next to the bridge and mute with your fretting hand, you can emulate john's tone pretty accurately on any guitar.
I like analogue Solid State amps that make no effort to be "tube-like", and I'm proud of it...

...A little too proud, to be honest.
#4
To be frank if you want a Rickenbacker similar to Lennon's without the hassle of short scale or fear of low versatility go with the Rickenbacker 350v63. They're pretty much the 325 with a longer neck, it has the same style as Lennon's but contemporized for modern play. you can do Beatles songs on it but other genres as well so versatility rides well there. The only downfall is the longer neck makes the body look kind of funny, but if the small disproportion won't bother you go for a 350.