Learn Italian: La ragazza è ossessionata a tal punto da pedinare il cantante. - The girl is obsessed to the point of tailing the singer.

Both structures translate to 'to the point of' or 'to such an extent that.' A tal punto da adds a bit more emphasis because of tal (such), highlighting the extreme nature of her obsession. Al punto da is slightly more neutral, but they are completely interchangeable here.

Why do we use the infinitive pedinare instead of a conjugated verb?

Because this is an implicit consecutive clause. When the subject of the main action (being obsessed) and the resulting action (tailing) is exactly the same person (la ragazza), Italian uses da followed by the infinitive. If the subjects were different, you would need an explicit clause with che and a conjugated verb, such as: È ossessionata a tal punto che i suoi genitori sono preoccupati (She is obsessed to such a point that her parents are worried).

Could I use così... da instead of a tal punto da to express this limit?

Yes, absolutely! You could say La ragazza è così ossessionata da pedinare il cantante. Both structures are implicit consecutive clauses used to express a result. A tal punto da just sounds slightly more dramatic by explicitly mentioning the 'point' or 'limit' that her obsession has reached.

Does the verb pedinare just mean 'to follow'?