Hi
The 2 requirments that will be difficult to satify are
Measure resistance down at 0.1
Measure diode voltage upto 5V (for tester zeners)
I do not think there are any dmm that can do the latter.
There are a number of projects or kits on the internet that do a device that measures diode voltage and zener voltage. I think some even go upto 20V
As ejeffery suggested, to measure low resistance accuractly, you will need a dmm with 4 wire measurement. As far as I know, only bench meters have this feature.
You can either look out for used ones on ebay.
Or cheap brands to look at
GW Instek
BK precision
I am not a fan of Rigol, Vichi or Uni-T bench meters
The suggestion for 2 dmm is also a good idea but having 2 may not satisfy your original requirements.
I do not think the ut61e can do either of the difficult requirements. I have one, the diode testing voltage is only 3V. Like all hand held dmms, they are not good at resistance below a few