Learn Polish: Paleontolog przypuszcza, że ten dinozaur mógł szybko biegać. - The paleontologist supposes that this dinosaur could run fast.

The verb przypuszczać (to suppose, to assume) expresses a belief that something is a fact, so it pairs with the factual conjunction że (that). Remember that you cannot skip że in Polish like you can drop 'that' in English, and you must always put a comma before it.

If the verb was wątpić (to doubt) instead of przypuszczać, would the sentence structure change?

Yes. While przypuszczać and twierdzić (to claim) state a belief and use że, the verb wątpić expresses doubt. If the paleontologist doubted it, you would replace że with czy (whether) or żeby: Paleontolog wątpi, żeby ten dinozaur mógł szybko biegać.

Why is mógł in the past tense when the main verb przypuszcza is in the present tense?

The paleontologist is making an assumption right now (present tense przypuszcza), but the dinosaur existed in the past. Polish does not use complex sequence-of-tense rules here; the subordinate clause simply uses the tense in which the action actually happened.

Why does this sentence use the imperfective verb biegać instead of a perfective form like pobiec?

The sentence describes a general physical ability the dinosaur had, rather than a specific, completed instance of running from one point to another. For general abilities, habits, and states, you always use the imperfective aspect.