1. EF pulls all the records into memory then performs the query operation. How EF would behave when table has around ~1000 records?
That's not true! EF fetches only necessary records and queries are transformed into proper SQL statements. EF can cache objects locally within DataContext (and track all changes made to entities), but as long as you follow the rule to keep context open only when needed, it won't be a problem.
2. For simple edit I have to pull the record edit it and then push to db using SaveChanges()
It's true, but I would not bother in doing that unless you really see the performance problems. Because 1. is not true, you'll only get one record from DB fetched before it's saved. You can bypass that, by creating the SQL query as a string and sending it as a plain string.