Balance shapes. If you make both of the inner forms (counters) of the 'B' exactly the same, the top counter will optically look bigger. Your character will look plumby, like it's falling down. If you make the top counter smaller than the bottom one, your character looks much more balanced.
The counter of the 'B' doesn't have to be exactly the same as the counter of the 'P' for example. If you would make them exactly the same, the right sidebearing of the P would be much too big. So you have to balance the black and white spaces in every character separately. However, there must be a relationship between the amount of white space inside a 'B' and inside a 'P'.
About making a lowercase 'r': it's not an 'n' with an amputated leg. Your 'r' can get very weak and soft in that way. You can make it much stronger if you let the ending of the 'r' follow the horizontal reading direction. In that way, the space on the right side of the 'r' will be more open, and more balanced. It will not disturb the rhythm of your type because the right sidebearing can be much smaller. The whole letter can be made more narrow as well. As a consequence the white space in the top of the 'r' could be has to be changed. In case you change that form, optically you'll not confuse the 'r' so quickly with the 'n' as well.
Kerning. Knowledge about kerning will give a deeper understanding of type. However, forget about kerning for now, spend your time on other things. It's much more important to properly space your characters.
A kerning pair is a technical issue for optical reasons. Simply said: when one certain character is followed by another character you can define a different space in between these two characters. This space can vary from the the normal spacing (right sidebearing of the first character + left sidebearing of the second character). The difference can be positive or negative; you can add more space for a certain combination or you can reduce the space. A kerning pair can technically be implemented in a digital font file.
In some cases kerning is inevitable and necessary. When a capital 'A' is followed by a lowercase 'v', a big white space will appear which cannot be solved by adapting the spacing of the characters. Changing the spacing would mess it up when they would be combined with other characters again. For this occasion a kerning pair is needed (see drawing). In the sketch you only see some examples where the kerning pair is negative; reducing space. But you can also imagine a positive kerning pair when a 'f' is followed by a bracket for example; "f)". More space has to be added to avoid those characters overlapping eachother.
Ligatures. In a very few cases they are essential. Some well known ligatures are 'fi' and 'fl'. The inevitable need for a ligature is depending on the design of a font. Not every typeface will need a ligature for a 'fi' combination. But in some cases the dot of the 'i' is interfering with the 'f'. Get rid of all that annoying row but making a ligature, one glyph which represents two (or more) characters. Next to a functional aspect, there is an aesthetic aspect of ligatures. You could create a ligature for a 'st' combination, or maybe for 'nky' or 'ism'. Anything is possible. Admitting that also this is not the most urgent issue in type design, it's another obstacle on the road to perfection!