Silicone does not paint easily, so keep that in mind. Dap 33 or Crawford's painters putty would probably be a better choice if you have lots of cracks and gaps. Usually the only sealant you want to use on glass is 100% silicone, and it is usually just a VERY fine bead around the perimeter. This is often best done after the windows have been completely painted, and a clear silicone is usually best. A caulking gun in the hands of a DIY'er is often a terrible thing.

The official name is Jalousie window. But generally i agree. Made for warm climates but sometimes seen in others. I'm sure you could rig something to work but a new door would be better. A box store might be able to tell you what size vinyl lite they could order... based on that info you could see if it would fit.

Building supply stores can get you new glass inserts if the size matches standard glass. To custom make an IGU for your door would probably not be cost effective. Standard Pre-hung Utility doors are not that expensive and DIY friendly. A solid door would provide the most protection against heat loss if you do not need the glass for visibility.