I’m no expert, but I’m fairly confident that the answer is a definite yes. While differences in upload and download speeds exist, the uploading and downloading will happen with the same client internet connection in most cases. If that connection sucks that means downloading new data from the server will also be slower than it would be to a client connected to a faster network.
Imagine you’re trying to shout information to someone. The farther you are away from them the more difficult a conversation gets, both due to them not being able to hear and due to you not being able to hear them.
There definitely is. You’re sending and receiving data from a server that is at a different location than you are. The data needs to travel through the internet. You measure that travel time with a “ping”.
I was lagging in a PvP game and while the characters were frozen, I was still getting damage done to me (I could see it happening). Which makes me think that server to client lag is super tiny, while client to server lag depends on your internet.
Let’s think about network connections as a doorway going from your apartment to the hallway. If the doorway is too small you will have trouble fitting through it and probably take longer - assuming you can get through at all. This is how a client-server connection works in a sense.
It doesn’t really matter whether you’re trying to get into your apartment (server to client) or whether you’re trying to get out of your apartment (client to server) either way if the door is too small you’ll take longer.