Specifically I'd like to know about the apparent joining of a dotted quaver and a semiquaver in the second row of my photo.
Is that what these are?
If that is what is meant then how does this differ from a separated dotted quaver and semiquaver?
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You're right it's just a dotted eighth note and a sixteenth note. The bar across the top is called a beam and it is typically used to group smaller notes by beats. For example that pattern in 4/4 would take up one of the four quarters note beats. Grouping them together clearly shows they make one beat in 4/4.
As Dom says, it's a beam. Beams will join notes (as long as they are smaller than crotchets!)to make patterns of beats. In 4/4 time they should join any appropriate notes to split the bar into 2 equal halves. It's not always written like that these days - but it does make things easier to read. Likewise, in a 2/4 bar, a beam would stretch for the equivalent of each beat. If the note values were small, they may go over each separate beat in 4/4.