If when your sim(s) goes to schoolor work, can you play them there?

You can play them going to work and even entering the building, but you can not play them at work.

No. But in the action queue, there's a little drop-down thingy and you can choose what they do there. Some examples of actions are:

Business as usual
Work hard
Take it easy
Meet co-workers
Chat with co-workers
Suck up to boss
And an extra thing but it varies depending on the job you choose