I require the correct and best front mech for t4010 crank (48t) with t4000 rear derailleur, shifter and Alivio cassette (9 speed). I'm struggling to get the t4000 FD with 63-66 degrees (assuming that's for hardtail), 48t and bottom pull. What are the alternatives??
There have been a number of 9-speed "T" series (trekking) front derailleurs in dual or bottom pull. For the most part they'll all work. The "T" is Shimano-ese for a cage profile whose radius is optimized for their 48/36/26 cranks and indexes properly with their mountain shifters (or perhaps more helpfully, with all their flatbar front triple shifters other than flatbar road ones). Confusingly, Shimano now has at least one front derailleur, FD-M371, that also is contoured for 48t but isn't a "T" model, which is a historical anomaly. FD-M371 is one of if not the only current production one does what you need it to do, but is only Altus level. FD-T4000 can still be had and is a little nicer, but appears to be out of production.
One of the curveballs with these cranks and front derailleurs can be that they are targeted hard at the European markets, although are not exclusive to them. If you're anywhere else, you might find limited options unless you pay extra shipping.
If you want the literal best and if the frame can take it (it probably can), it tends to be a little better in terms of feel at the shifter to get a dedicated bottom pull, high clamp model. I don't think there are any 9-speed ones of these in current production.
I believe that either the LX-level FD-T661 is the highest end ever trekking specimen, or if there was a 9-speed XT-level one at some point it's very old now and my US-ian eyes have never seen it.