I have a 3 foot tripod I would like to mount on my roof however I only can mount the ham IV rotatorabove the tripod because it will not fit inside the 3 foot tripod. I would like 2 mount a 10 meter to element aluminum moxon a 2 element. 6 meter aluminium moxon, and a 15 element. 2 meter yagi...
Questions:
Can these antennas be safely supported, assuming the tripod is properly installed
Depends on what you call properly installed. IMO that is far too much windload for a simple tripod mount unless you installed 2x4 or 2x6's across the rafters inside the house and bolted securely thru the roof and into them. Not lag screws either but bolts with large washers and nuts on the inside of the roof.
Will it be doable to mount these antennas on an unsupported mast mounted directly to a ham iv?
Again IMO no. You want to mount a two element 10m moxon, a two element 15m moxon, an unknown size 6m moxon and an unknown sized 2m yagi all on an unsupported mast on a tripod? The spacing would be next to nothing along with the associated problems of that or the long mast will not last in the wind and will likely damage the tripod as it all comes down.
How tall should the mast be to support these antennas?
A LOT longer than the tripod can handle and it cannot be simple swaged type masting either. The antennas will work close spaced but tuning and interaction will be quite an issue and performance will suffer. Ideally you would want to minimize this and placing the 15m at the bottom followed by the 6m, then 2m then finally the 10m at the top would be the best arrangement for minimising interaction of the 10 and 15m antennas but it places a higher wind load on the top of the mast. Placing the 15m at the bottom, then the 10m, then the 6m and finally the 2m minimizes the wind load but greatly increases the problems with the 10 and 15m antennas being so close together.
I understand the frustrations of stacking antennas and trying to stuff 10 pounds of crap into a 9 pound bag myself. I am currently trying to figure out how to stack an Explorer 14 for 10/15/20m with 40m kit installed, an A3WS for 12/17m, a six element 6m homebrew yagi, and a pair of 13B2 2m yagis for 2m SSB and possibly a Cushcraft A147-11 for 2m FM all on as short a mast as I can muster. I will have interaction I know but the minimum I can get it all down to is 15 feet above the top of the tower. It should be much more than that ideally but I don't live in an ideal world.
How tal of a mast can the rotor support?
That all depends on the wind drag. The more wind the shorter the mast. A rotator mounted on the end of a piece of pipe will have no where near the capacity as one mounted on a flat plate inside a tower with a thrust bearing of some type to take the sideways stresses off of it. IIRC a Ham IV can handle 15 sq. ft if tower mounted but only half that if mounted on a pipe and that assumes the mast is only a few feet long.