If the roof has large purlins to support the rafters, the ceiling joists don't have much work to do except hold the ceiling up, so may be quite small with hangers to the purlins. (However, ceiling joists may also be the horizontal brace that stops the roof spreading - it depends how the roof is constructed). If you intend to use the loft for storage then cross "battening" will certainly add strength. The joists are also unlikely to be in quite the right place for boarding (because you need to support every edge to avoid cracking). You can trim board to odd sizes, but better to add additional timbers and noggins so that the board edges are neatly secured. When they constructed lath ceilings, the spacing of joists didn't matter, so they may be quite variably spaced.
They may well be loose because old fixings have perished, particularly where the joist end sits on a wall plate in the eaves. Easy to rectify. Don't bother drilling pilot holes - use good sized and quality screws (e.g. reisser cutters) and drive them in with an impact driver - as said above on the skew is fine. As said, if joining large timbers together side by side, coach screws with hex heads are useful. Think whether the screw is doing a structural job or just keeping something in location.
Putting in the timbers and screwing the plasterboard in place is well within DIY capability - use plasterboard screws not regular countersunk - take time to do it neatly. Plasterboard is also available in 900x1800 which is easier to handle than 1200x2400 (note PB is usually this size and not the imperial 8x4 equivalent 1220 x 2440) Your plasterer can then come in and skim it all up. Job done.