this page has a good writeup on page splits:
but if you think of it like a phone book, with each page in the phone book holding 8 KB of data, a page split occurs when data is added or changed on a page that causes it to go over the 8 KB. So, in your example, inserting into the C's may not cause a page split or it might even though it is in the middle of the table. If the C's page has 5 KB of data on that page and you are inserting 1 KB of data, it won't cause a page split. If it has 7 KB of data and you are inserting 2 KB of data, you will get a page split. If the row has 1 KB of data in it and the page has 8 KB of data in it and you update the data in the row to be 2 KB, page split.
Paul Randal has a good writeup on good page splits and bad page splits too. But basically, a good one is when it happens at the end of the index because you just put the data onto the end and no shuffling required. Bad ones are when it happens in the middle of the index because you need to shuffle the whole table around. LINK - https://www.sqlskills.com/blogs/paul/tracking-page-splits-using-the-transaction-log/
Fill factor only comes into play when the index is NEW or REBUILT. Basically, it is just telling SQL that the data is either changing frequently or the inserts happen at random locations in the index so save some space on the page for these changes. Microsoft says "When an index is created or rebuilt, the fill-factor value determines the percentage of space on each leaf-level page to be filled with data, reserving the remainder on each page as free space for future growth. For example, specifying a fill-factor value of 80 means that 20 percent of each leaf-level page will be left empty, providing space for index expansion as data is added to the underlying table. The empty space is reserved between the index rows rather than at the end of the index." and I think this covers it fairly well. LINK - https://docs.microsoft.com/en-us/sql/relational-databases/indexes/specify-fill-factor-for-an-index?view=sql-server-ver15
The TL;DR version:
Page splits happen when a page is filled and a new page needs to be added to the index. Doesn't matter where you are inserting the data; just as long as a new page needs to be added.
Fill factor is used when creating or rebuilding an index to define how full the pages should be and to allow (or not allow) growth on a page. Page splits should generally decrease if you have a proper fill factor set, but it can result in unused space in the database.
If you think of it like a notebook, if you write until the page is 50% full, you have half a page left for notes if you need to go back and make changes or additions. But if you never need to make changes or additions, half of your notebook is unused. On the other hand, if you fill up every page 100%, and you need to go back and make a change or addition, you have no room for additions or changes. YOu would need to add a new page into the middle of the notebook. Which is also a good analogy for page splits. Page splits are when the page gets full and you need a new page. It is much easier to add a page to the end of your notebook than it is to add one in the middle.