OK, let me see if I can clear this up. The #1 consideration around which pivots all these decisions is the number of live, acid producing bacteria. In your cheesemaking, this should be consistent in terms of the bacteria count per pound of milk, so you can achieve consistent results.
The way this is measured, and I don't think manufacturers talk about it because it's sort of a geeky thing, is the number of colony forming units (CFUs) per gram of whatever culture you're adding, fresh in skim milk, cultured in 11% skim starter base, bulk frozen, or DVI/DVS. A CFU is just one active, viable, living, and non-damaged bacterium.
I've posted these levels before in various posts if you want to go back and read about more of how they're used and what they mean. And I'll post them again for your ease.
A DVI culture has anywhere between 1x10^ 11 (100 billion) to 1x10^12 or 10^13 (trillion, or more) CFUs/gram. A regular culture like yogurt or buttermilk, when very fresh has about 2x10^9 (2 billion) CFUs/gram. More if the the milk has a high protein content.
So what does this all mean? Simply that there is not a 1:1 relationship between a fresh prepared culture and a DVI. A yogurt culture may be old, frozen, or have high proteins, so the live bacteria may range anywhere from 500 million to 4-5 billion. Bacteria multiply every 20 minutes, so if you were in your recipe to use a yogurt with low bacteria count, it would take a few hours to get it to the right level as if you had used a fresh starter (like yogurt). Same for DVI. DVI culture will range from 100+ billion, to sometimes a trillion or more. That's why you need to weigh out the entire packet of DVI culture and resize. End point, there's no good way to have some sort of repeatable conversion between fresh culture and DVI UNLESS you use the same processes every time. For example, you always use only fresh culture and fresh DVI. Then you can get reliable comparisons.
Now let me answer your other questions. Sorry this is long, but it's vital to cheesemaking.
1/4 tsp of culture is about .75 grams. At 150 billion CFUs for the DVI, it will take about 75 grams of fresh starter to equal the same amount of bacteria. That's about .333 cups. If you are using frozen cubes, that depends on so many factors. For example, concentration of original culture, method used to freeze, temperature used to freeze, method of storage, length of time in freezer, etc. But figure about double the amount of fresh culture, maybe a little less or more.
Yes, for fresh starter, you increase is proportionally per gallon. Not exactly the same with DVI. You don't use 1 tsp per 4 gallons of milk, for example, because it's so concentrated. More like 1/2 tsp per 4-6 gallons.
Yogurt has thermophilic bacteria, so yes it is one example of thermophilic starter.
tally, some aspects are proportional... milk behaves differently in bulk. It's actually easier to use more than less. In general, use these as your starting point for most cheeses: 9-10 ml single strength rennet per 100 lbs of milk, or 4-5 ml double strength. and 1-2 DCU/Units per 100 lbs of milk. Resize from there to get the right amounts. I will add that the amount of culture changes with cheese types. Some use more, like cheddar, and some use less, like tomme. But those cultures for those cheeses also have different acidification curves.
Hope this helps.