Welcome, Ben! These are some good questions. I'll give a stab at them if that's all right. Deciphering notation can indeed be rather frustrating...
In the first example, I believe that the 253 is a fingering for the trill below it. Instead of using a 232 trill fingering or another more traditional fingering, the editor or composer suggested a more unusual fingering in order to achieve a certain effect or make a certain technical issue more easily surmounted.
The double colon you are referring to in example two is denoting that the quarter notes of your chord are double-dotted quarter notes. A dot after a note extends the time of the note by half. If the first dot is followed by another dot, then the second dot extends the length of the original note by one-fourth. That means that the chord in your example gets seventy-five percent of the original quarter note value added to it to make the note one and three-fourths beats (equivalent to one quarter note and three sixteenth notes). I suspect that the double-dotted quarter note chord is followed by a sixteenth note or sixteenth note chord to make the two notes or chords two beats in all.
In order to explain your third example, we must remember that there are, generally speaking, three basic types of articulations in music: staccato, legato, and portato. Staccato is short and detached (often indicated by a dot), while legato is tied and smooth, with no breaks between the notes. (we can often tell that by a slur). The third type of articulation is like a "heavy staccato" or "sticky staccato," a longer sound than staccato but with small breaks between notes. Oftentimes, portato is indicated in musical passages by staccato markings with a slur over them. That's what you have here in your example. It is, essentially, a slurred staccato.
I hope my answers were helpful to you, and feel free to tell me where I wasn't clear. All the best to you in your musical endeavors!