Can I model and analyze a multi-storey timber building in ETABS? Of course you can. ETABS doesn't have much in the was of DESIGN or code checks for wood members. But, analyzing wood is certainly possible.
From where can I get the proper timber material properties? This is where it gets tricky... YOU have to enter you wood material properties correctly to get good analysis results. Which means wood beams and columns will have different material properties based on their species, their size and their grading.
If you have shear walls (or diaphragms), you will have to adjust the material properties based on the thickness of the sheathing, the type of sheathing and the nailing. I believe the NDS' Special Design Provisions for Wind and Seismic has some examples on how to do this.
Since the building has no steel or concrete will it be able to sustain lateral and gravity loads? Well, it will have concrete foundations. Steel connections, anchors and such. But, the key to whether it can sustain the loads is YOU and how well you design it.
For what it's worth, if you're not experienced with wood, then I'd suggest starting with smaller project. Like designing a portico, deck or patio cover. Maybe designing a wood diaphragm for a warehouse or something. It's not crazy complicated, but the load paths can get a little tricky.