260 nm to 350 nm is alright. one can use LED source too to avoid heat

This is YOUR job to find a reference or to calculate the value (which is trivial) 

you can calculate it by computing bandgap of your lab prepared TiO2. E= hc/lamda.. Once u would have E, wavelength u will get.. Search google scholar any paper related to tittania and photocatalysis.

depends on your catalysts structure which is usually anatas or rutile you need a source to generate photons with the sufficient energy to excite the electrons which is in this case a source with a wavelength shorter than 385nm using this equation (1240/eV= wavelength (nm) ).

Note that various catalyst have different absorption properties based on variety of parameters like synthesis method, DOPANTS, or calcination temperature...

Pure titanium dioxide is activated at about 380 nm radiation