Latin Names and Nomenclature Questions…

I posted the following in the Gardening community ( link )

Hello Fellow Plant-lovers… I’ve just began to get interested in the Latin names of my various plants and have a few questions about nomenclature. Please forgive me/correct me if I’m using the incorrect terms.

I’m using these 6 examples for the questions below:
a. Kalanchoe tomentosa
b. Crassula perfoliata ‘Falcata’
c. Crassula perfoliata var. falcata
d. Crassula perfoliata falcata ‘Morgans Beauty’
e. Crassula perfoliata ssp. falcata
f. Crassula lycopodioides f. variegata

I generally have seen the Latin names as [Genus species] as in (a). I’ve also seen [Genus species ‘Something’] as in (b).

1. Is the ‘Something’ between the single quotes called a “cultivar”?

Today as I was surfing Google, I ran into a couple of unfamiliar nomenclatures (c-f)

2. Is (c) equivalent to (b)?… and what does “var.” mean?
3. In (d) they have 4 terms. Is this a correct usage?
4. In (e) and (f), what does “ssp.” and “f.” mean.

Sorry, if I sound so elementary. I’ve generally been using the common names of my plants, but recently discovered I have a couple of plants that have the same common name, like “Jade Plant”.

Thanks in advance for all your help.

Also, if any one of you is good at identifying plant names, I have a photo set on with plants I can’t identify. You can check it out here. ( link )