Aberdeen Pier Ferry to Lamma Island

From Aberdeen Ferry / Kai to Pier, Aberdeen Praya Road, Hong Kong to Lamma Island, Hong Kong. You can go a lot of places from Aberdeen Pier in Hong Kong, though they are mainly outlying islands.According to the Transport Department in Hong Kong, there are two franchised/licensed ferry line that departs from Aberdeen Promenade that gets you to Lamma Island:

1. Aberdeen – Yung Shue Wan via Pak Kok Tsuen
2. Aberdeen – Sok Kwu Wan (via Mo Tat)

Furthermore, according to Traway Travel Limited, they operate two more routes (in addition to 1.) from Aberdeen as of 2019:

3. Aberdeen – Stanley / Po Toi Island
4. Aberdeen – Cheung Chau (Alternate link)

There are also two river crossings (kaito) routes between Aberdeen Promenade and Ap Lei Chau (main street), and a ferry service that gets you to the Jumbo Kingdom, a pair of floating seafood restaurant nearby.

The OP also asked:

Are there ferries from Aberdeen to […] Mui Wo (or other parts of the Lantau Island), or to Central, or to the Kowloon Peninsula?

As of 2019, no, at least not directly:

• Mui Wo is served by ferries to/from Central, Cheung Chau and Ping Chau only (Link to the ferry wiki in Hong Kong, Chinese only);
• Central is better connected via minibuses; and
• By extension, Kowloon Peninsula, which is further to Aberdeen in Central, is too far to make travelling by boat practical.