Learn Russian: Мы собираемся посмотреть маршрут по карте.

While на карте (using the prepositional case) indicates a static location like 'the city is on the map', по карте uses the dative case to show how you navigate or get information. The preposition по often translates to 'by means of' or 'along', so here it implies you are figuring out the route by means of the map.

Doesn't собираемся usually mean 'gather' or 'collect'?

It can mean 'to gather' for a group of people, but when followed by an infinitive verb like посмотреть, the reflexive verb собираться means 'to plan to' or 'to be going to' do something. So мы собираемся посмотреть means 'we are planning to check'.

Why use the perfective verb посмотреть instead of the imperfective смотреть?

You use the perfective посмотреть because you are talking about completing a single, specific action with a result (checking the route once to know where to go), rather than the continuous or repeated process of looking at it.

Why doesn't the word маршрут change its ending here?

Маршрут is the direct object of the sentence, so it is in the accusative case. Because it is a masculine, inanimate noun (a non-living thing), its accusative form is identical to its basic dictionary form.