Learn Turkish: Memnun oldum, hoş geldiniz. - Pleased to meet you, welcome.

Even though you feel pleased in the present moment, Turkish uses the past tense here. It literally means 'I became pleased' the moment we met. This is a fixed phrase, so it is best to just memorize memnun oldum as the standard way to say 'pleased to meet you'.

Why does geldiniz end with -iniz? Are we talking to more than one person?

It can be both! The ending -iniz is used when talking to multiple people, but it is also the polite, formal way to address just one person. When you meet someone new, using the formal hoş geldiniz is the standard polite greeting.

What do the words in hoş geldiniz literally mean?

The word hoş means pleasant or nice, and geldiniz is the past tense of gelmek (to come). So literally, you are telling someone 'you came pleasantly' or 'it is nice that you came'.

Can I use memnun oldum to say I am happy about other things, like getting good news?

While memnun means pleased or satisfied in general, the exact phrase memnun oldum is almost exclusively used as 'pleased to meet you' when introduced to someone. To say you are happy about an event or news, you would normally use a different phrase, like çok sevindim.