What am I supposed to do with the pressure plate and statue for ‘The Ultimate Heist’ quest in Oblivion

Most Oblivon bug workarounds are sadly unavailable on the console versions, as they require use of the developer console.

The only "leveling problem" with Oblivion is if your chosen class focusses solely on "soft skills" that are nigh useless in combat, such as Security, Speechcraft, Mercantile, etc. and has no damage dealing primary skills. If so, then you can easily end up leveling up using lockpicks, conversations, and haggling, while your combat skills stay low. Since the game adjusts the levels of your enemies according to your level (which does not necessarily reflect your strength in combat) you may end up to weak to beat them.

However, since you can adjust the difficulty settings anytime this is not really that much of a problem. Also, you can even use this mechanic to your advantage by raising only non-primary combat skills. Hence, your level (and the level of your enemies) will stay low while your strength in combat rises. This will make the game even more easy.

Having said that, I of course suggest to stop worrying about such issues and to use the "play as you like" leveling system to maximize your fun, not your stats. To this end, any moderately balanced character will do quite fine.