You can pot up the pups separately or leave them in the pot they are in. When the pups are at least 1/2 the size of the mum, cut her out and top up the mixture. You can go a bigger pot if you want.
Hopefully they will all flower together but you will have to repot them all after they do.
Sorry I can't help with fertilizer as I don't know your brands.

I had the same dilemma a couple of years back; A plant I had previously bought just for the nice yellow flowers had finished flowering and the mother was producing three small pups. and being a Neo. grower and having very little experience with Guzmanias, I decided to just cut off the old inflorescence and put the whole plant into a larger pot with fresh potting mix, mother, pups and all.

I gave it a hefty dose of Osmocote "High K" and put it in the shade house with my Vrieseas beneath 75% green shade cloth and forgot all about it. That was until I saw something yellow amongst the leaves and on investigation found three nice fat inflorescences. I moved it to a more forward position where it would get better light and about three months ago they all flowered. After a month or two in the house it still has the nice lemon/yellow bracts and is now the centre-piece of the Vriesea house.

As Sunshine says, you can pot up the pups separately or do as I did and leave them all together, the choice is yours; but remember to give them a bit of fertilizer as I have found they respond to feeding better than most other brom's do.

All the best, Nev.