Reference to elastic documentation:
Refresh API

?refresh

Empty string or true
Refresh the relevant primary and replica shards (not the whole index) immediately after the operation occurs, so that the updated document appears in search results immediately.

Now consider the scenario,

I have a 3 node cluster.
I have a index say Index A having one shard, 3 copies 1 master copy and 2 replica copies.
Suppose there is a high amount of lag in replica copy of Node 3,

Q1. Will the writes be acceptable ? Writes are govern by which config
and what is the default value of it? Is it 1 (master only) or is it quorum ?

Q2. If writes will be acceptable, and Node 3 is lagging, can coordinator node send the request of search to Node 3?

Q3. Replication happens using translog only as per my knowledge ?
And Node 3 already has lag, so it wont be able to process the logs of segment creation as well.

but according to elastic doc when ?refresh=true is triggered it is ensured that document is available foe search

Reference to elastic documentation:
Refresh API