What does Long Call EURUSD mean? Does it mean Long Call EUR and Short Put USD? When we draw payoff do we consider only w.r.t. to CCY1 i.e. EUR in this case?
First please keep in mind that EUR (and GBP) are quoted "cable". So if the USD EUR exchange rate is quoted as 1.1, for example, that means that (quotation or countercurrency) USD 1.1 = (base currency) EUR 1. Most other currencies are quoted the other way, so if the USD CHF rate is 1.1, that means CHF 1.1 = USD 1.
An investor is "long" an option means that the investor has bought the option, paid a premium, and now has the right, but not the obligation to exercise the option.
If you're long a EURUSD option with the strike 1.1, and you can exercise when the spot rate is 1.2, then your option is in the money. You will pay USD notional (you're effectively long a USDEUR put..) and receive EUR notional (= USD notional / strike), which will be more EUR than you would have received using the spot rate in the market.