1. I have connected 5V to common anode of 3 segments but it is driven by 3.3V MCU.
2. Also tried removing by R11,R16, & R17 but its not working. What could be issue here?
3. As soon as I turn high(3.3V) on T1,T2,T3 all segments get together.
Are you saying all come on even if T1 T2 T3 are at logic HIGH. That's not surprising.
If T1 is at 3.3v and the base of the transistor is at 5 - 0.7 = 4.3v then there is 1v over your 2k2 base resistor which is about 500uA, easily enough to turn the transistor on and with a gain of 100 or more that's 50mA collector current.
Try a couple of small diodes (eg 1N4148) in series with the 2k2 resistor so the logic output needs to go below 2.1v before base current will flow.
That works too. It depend on whether the TS wants to change his logic/code. Personally I would, as negative logic always annoys me.
For completeness, using the original logic, here's the one extra component solution... using a 2.4v Zener diode (plus change the base resistor to 1k5 for a little extra drive to run the segments at 15mA, or leave at 2k2 for 10mA/segment).