I think I can help explain all but your 3rd question.
- A transgenic mouse will typically have the genetic construct in all cells. Unless you get a chimeric animal, which is screened for during the making of the mouse.
- VIP::Cre means that the promoter of VIP was used in front of the region of DNA that encodes for Cre recombinase. Note, the animal still has the endogenous VIP gene that makes VIP. This is an additional construct. The intent of this kind of system is to limit the expression of Cre recombinase to only the cells that would also be expressing VIP.
- LSL stands for Lox-Stop-Lox cassette. LSL:TOM is the gene that encodes for tomato red protein with a premature stop in the transcript such that it never makes a correct protein (and no red).
- If Cre is expressed in a cell with the LSL-TOM construct, it will recombine the LSL and remove the stop codon, thus enabling the creation of functional tomato red transcript and fluorophore (protein). Again, this construct is in the DNA of ALL cells, but the recombination event (and subsequent expression of function TOM) will only happen in the cells that are also expressing Cre recombinase. And for a VIP::CRE mouse this only happens in VIP expressing cells.
1) Actually every cell in the animal has a VIP::Cre (excepting blood of course or sex cells that got the non transgene allele during meiosis. This is because usually the cre genes are kept at Hets during mouse mating).
2) All neurons (and all cells; see answer 1) will contain the genetic construct VIP::CRE. The intent is in the VIP::CRE mouse, only cells that would express VIP would express Cre recombinase. This means that other tissues in the body that express VIP should also fluoresce red in a VIP::CRE/LSL-TOM mouse. As an aside, all cells that normally make SOM should also be making GFP in the SOM::GFP mouse, but every cell will have the DNA transgene.
3) This question is outside my breadth of knowledge. I've done lots of work with transgenic mice, but other than looking up that that viral construct has something to do with calcium and imaging in neurons, I am not sure.
Per Bryan Krause: "...the expectation is that it will infect most if not all cells, not even just neurons, but it is using the 'synapsin' promotor which is neuron-specific (but would be expressed in both VIP and SOM cells, as well as other neuron types). Presumably the authors are using calcium imaging to detect activity across a whole mixed population but then using tdTomato to identify one subpopulation or the other, depending on which animal is used."
4) For VIP-cre::LSL-TOM::SOM-GFP(GIN). As written, this would imply the expression of Cre is necessary to activate transcription and encoding of tomato red in VIP expressing cells. But that GFP is already active in SOM expressing cells from day one of development.
Some uses of Cre-Lox systems are illustrated here. This picture from that website demonstrates graphically what is going on with a LSL construct.
Your system has tomato red instead of lacz and is using VIP expressing cells as a targeted system.