There are lots of ways you can play a 'six string' e minor arpeggio, and just because one particular method involves the use of the septuplet (7 note per beat) doen't mean you shouldn't practice it.
7's are hard at any tempo, and are hard slow because as you said you need to divide the subdivided beat into 3.5 - for me I find the only way is to practice a lot and you will get the feel of it.
Just practice saying "dirty hippopotomus" over the beat and this seven syllabal phrase will help you get the timing - aim to get each septuplet the same length - don't make it a 4 demisemi/3 semi triplet grouping as this is wrong.
I don't have a guitar with me so I may say some mistakes.
Something a great guitarist once told me was that he kind of 'forces, and squeezes' extra notes into a space otherwise too small for them, so rather than strictly thinking in 7 you can do a quasi accellerando (kind of speed up) the notes in the middle of the beat - a la rubato - steal, or rob some time from the next note in the lick to make the others fit the beat.
A way to make that second Em arp work in semiquavers or any regular multiple of 4 is to repeat the lowest and highest notes as you reach them.
So you play the 12th fret low e, ascend through to the high G on the 15th fret high E string, repeat this note, descend, reach the low E 12th fret, repeat this note and ascend.
Experiment with fingerings - get a tab book and sit and evrytime you 'invent' a good fingering for something jot it down in your book.
Rather than seeking the answers from other people, work it out by yourself and you will have a far deeper understanding of what you are doing and why you are doing it.
The problem with the harmonics is down to your technique - you need to mute any unwanted strings, and this goes for any thing you play!
One of the secrets to good
sweeping is the muting of unwanted sounds - this stops the notes 'bleeding' into one another.
Yes this is a hard shape as you have a half barre at the 12th with you first finger, and a 'roll' in the 3rd(?) finger at the 14th - any time you need to barre or roll it makes sweeping a lot harder to keep clean - this is what separates the men from the boys - those that 'hear and fix' the problem, and those that either don't hear or are too lazy to fix it.
I hope this helps somewhat