1 Assuming these are friction pegs, slacken off the screw until they turn a little more easily. Once the strings are up to tension, you need to adjust this screw until the pegs hold, but can still turn freely.
2 How to attach the strings depends on your tailpiece - lots of different designs around. You shouldn't need loop end strings, just ordinary uke strings, and if they're not slipping that's good enough. Search online for prettier ways of fastening.
3 The banjo head must be reasonably taut - it should ping if you tap it with, say, a pencil, rather than going thud. Tighten opposite fittings by 1/4 turn at a go, working round the head.
4 The bridge must be in the right place or your intonation will be completely off. Measure from nut to 12th fret, and initially place the bridge the same distance away from the 12th fret. Put some tension on all strings, then bring one of them (say, E) up to pitch. Play the note open and at the 12th fret. Are they the same but an octave apart? If the 12th note is sharp, move the bridge a little towards the tail. If flat, move a little towards the nut. Once it's right bring all strings upto tension (they will try to tilt the bridge until it falls over with a scary bang, so ease it back upright from time to time). Fine tune intonation by nudging bridge back or forth as required. Then mark its position with a couple of faint pencil lines for next time you change strings.
