1) There are no obvious differences in the meaning between these two sentences, but I think "Help me tidy up" is more common. 2) Some medal (verb), such as: must, can(could), may(might) and so on, but " ought" is an exception, we often say" ought to do sth." Causative verb : let, leave, make , keep and so on Sense Verbs: see, watch, look at, notice , observe, hear, listen to, smell, feel, find....

There is no difference.

modal, not medal