Learn Russian: Осенью я работаю много.

Осень is the basic noun meaning 'autumn'. To say 'in autumn', Russian changes the ending to make it осенью (using what is called the Instrumental case). You will see this pattern with other seasons too, like зима (winter) becoming зимой (in winter).

If I wanted to say 'I like autumn' using this lesson's grammar, would I use осенью?

No, you would use the basic Nominative form: Мне нравится осень (literally 'Autumn is pleasing to me'). The form осенью is only used to say that you do something in or during the autumn, not to talk about the season itself as a subject.

Why does the verb end in -ю (работаю)?

The ending matches the subject я (I). For regular verbs like работать (to work), you drop the -ть from the dictionary form and add -ю to show that 'I' am doing the action.

Can I say я много работаю instead of я работаю много?

Yes, absolutely! Russian word order is very flexible. Both options are perfectly correct. Putting много at the very end just gives a little extra emphasis to the fact that you work a lot.