Learn German: Die Lesung, welche morgen stattfindet, ist kostenlos. - The reading, which is taking place tomorrow, is free of charge.

Both mean 'which', but welche belongs to the welcher/welche/welches group of relative pronouns. These are used in formal or written German as stylistic alternatives to der/die/das. Writers often use them to avoid repetition. Saying Die Lesung, die... puts the same sound back-to-back, so Die Lesung, welche... often sounds more elegant in writing.

How do we determine the exact ending for welche in this sentence?

Like all relative pronouns, it takes its gender from the noun it describes (die Lesung, meaning it is feminine) and its case from its grammatical role inside the relative clause itself. Here, it is the subject of the clause (the reading is what is taking place), so it takes the nominative case. The feminine nominative form is welche.

stattfinden is a separable verb, so why is stattfindet written as a single word here?

In a relative clause, the conjugated verb is moved to the very end of the sentence. When a separable verb's conjugated stem (findet) gets pushed all the way to the end and bumps into its prefix (statt), the two parts reunite and must be written as a single word: stattfindet.

Could I use umsonst instead of kostenlos here?