The sentence is mostly correct. I have no idea what a radio car is.

The verb to conjugate in this sentence is "watches" because Henry is the subject of the sentence. The other two verbs, smile and toss, are not performed by Henry.

Yes, using smiling and tossing would be correct, it would be a flowery way of saying it however.

It is impossible to use the present tense to talk about more than one action.

Here in this sentence we have two actions , one must be simple and the other must be continuous.

So you have to use the suitable tenses ( present , past , future ) .

Example: if Henry and Jimmy are using to do that every day so you can say ( Everyd Henry waches when Jimmy is smiling and tossing ,,,,,,,,, etc , we used present simple tense and present continuous tense.

But if they did it in the past so you have to say ( Henry watched Jimmy when Jimmy was smiling and tossing ,,,,, or you say Henry was watching when Jimmy smiled and tossed ,,,,, .

Smiling and tossing a couple of cartons of cigarettes in his radio car.

You are speaking about jimmy so pronoun must be his not their.