Were cult images (e.g. statues of gods) carried by a Roman army (or its commander) around 200 BC? If so, which gods? And were would they be kept while in camp? (I am not referring to items individual soldiers might have, but rather to objects officially belonging to the army, or to its commander personally.)
Cult images and altars were certainly carried by the Roman Army at that period. Commanders were allowed considerable autonomy, but that autonomy was, in practice, constrained by religious auspices. The situation is described in some detail in Chapter 3 of The Peace of the Gods: Elite Religious Practices in the Middle Roman Republic by Craige B. Champion.
Exactly which gods were carried is uncertain, but might well have varied by legion. I don't think any author from the late Republican period recorded exactly which cult images and altars were carried by any Roman army.
Our best information about the layout of Roman military camps in the late Republican period is probably to be found in the text De Munitionibus Castrorum ("Concerning the fortifications of a military camp"). This text dates from rather later than your period of interest, probably being written somewhere between the late 1st to early 2nd century AD, but it is probably as close as we are able to get.
It states that:
Aris institutis in praetorii parte ima, auguratorium parte dextra praetorii ad viam principalem apponimus, ut dux in eo augurium recte capere possit; parte laeva tribunal statuitur, ut augurio accepto insuper ascendat et exercitum felici auspicio adloquatur.
"The altars will be set up at the end of the praetorium; we will assign the auguratorium to the right side of the praetorium next to the via Principalis, so that the general can observe the omens there correctly; the tribunal is set up on the left side, so that having observed the omens, the general can ascend the tribunal and address the army on the favourable auspices."
- (my translation)