The easiest way to gain advantage on a death saving throw is to use inspiration.
If
you
have
inspiration,
you
can
expend
it
when
you
make
an
attack
roll,
saving
throw,
or
ability
check.
Spending
your
inspiration
gives
you
advantage
on
that
roll.
Alternatively, you could be a Wild Magic Sorcerer, and use Tides of Chaos. Well, probably.
Starting at 1st level, you can manipulate the forces of
chance and chaos to gain advantage on one attack roll,
ability check, or saving throw.
The 3rd- level spell Beacon of Hope explicitly grants advantage on death saving throws for its duration.
Fighters can use Indomitable to reroll a failed saving throw - not precisely the same as advantage, but pretty close.
Beginning at 9th level, you can reroll a saving throw that
you fail.
There are almost certainly more options that I've missed - getting advantage on things is a pretty fundamental part of 5e.
The asker mentions he is using a house rule:
after reading your answers and re-read the PHB. We were rolling D20 for hit on every spell then a saving throw(if applicable) on hit.
From that, it's hard to say anything about how this rule works. We have had a DM ruling something along these lines in another question. As I mention there, this is a huge nerf for spellcasters in general. About your question:
There are no (default) rules for advantage for attacking from behind 1
One option we have is an optional flanking rule, which still requires another enemy close to you in order to actually give advantage. You can read more about it here. D&D usually assumes that the character has a 360 degrees field of vision, even if they are facing a specific direction in the grid, for the purposes of being attacked. There are also optional Facing Rules (DMG p. 252), which states
A creature can normally target only creatures in its
front or side arcs. It can't see into its rear arc. This
means an attacker in the creature's rear arc makes
attack rolls against it with advantage.
It is still unclear about an attack from behind coming from a PC that is in the front arc, as it's not a situation that would be usually happening. This is not comparable to casting a spell with an actual attack roll because then the spell would be coming from the same direction as the PC (i.e., front).
So, in general...
Your DM is making a lot of house rules.
Is that a problem? Up to your group. If you, or anyone else, is feeling that these house rules are making the game less fun, unfair or similar, talk to your DM and state your concerns. From my experience, new DMs sometimes make house rules without fully understanding the mechanical consequences of these house rules. Explaining that his modified rules are hurting your fun is usually the best way to make them see it.
You also mentioned your group is new to D&D 5e, while it's not clear if that's true for the DM as well, it is possible that he is not aware that he is using house rules. If that seems a possibility for you, check with him if he knows these rules are not official. Sometimes, simply stating "Hey bro, that's not how it works" is enough for the DM to notice "Whoops, I was thinking about other random system". I myself carried misconceptions from 3.5e to 5e when it was released.
Sadly, as these are house rules, we can't answer, from the rules perspective, more than "none of these rules is stated in the books" and "your DM is the one who makes the rules, so if he said it, he's kinda right" (but he should be consistent - if your spellcasters cast a spell on the enemies' backs, you should get advantage as well). You can make a different question asking whether or not these house rules are balanced and how they impact the game overall, but, as I said, this is a different question.
As a side note, although the Shatter spell is mentioned, the actual problem seems to be about the house rule. Shatter itself could have been a fireball or any other AoE spell.
As a second side note, the Facing also states
A creature
can also change its facing as a reaction when any other
creature moves.
While "moves" probably means actual movement (walking from a square to another), if the DM is applying the same rule for AoE spells cast in a point of origin behind, he probably should allow you to react and change the direction you are facing to your back, when you see the spellcaster moving his hands and speaking some awkward phrases.
1 Note, however, that a specific rule is not required for Advantage/Disadvantage, as PHB p. 173 states
The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.
This is more a fall-back rule and a reminder that "the DM is in right to rule anything as he wants, to be frank", though, from how I read it.
Best Answer
Theory
The first thing we'll look at is a table that represents the odds of rolling at least a given DC, given a d20 with or without advantage (no modifiers yet).
A +1 to a non-advantage roll will always improve the odds of rolling a given number by exactly 5 percentage points. Conversely, a +1 to an Advantage roll will increase your odds by an amount equal to moving up one row on that table: a DC7 check made with +1 is equivalent to a DC6 check made with +0. A DC20 check made with advantage and a +1 modifier is equivalent to a DC19 check made with +0, which constitutes a 9.250 percentage point improvement.
There are a few casual observations we can make:
Practice
So back to the original question: Given two rolls, 1d20+x/Adv, and 1d20+y/NoAdv, which is better? Well, as established, it depends on the DC of the check, but to get the results from this table:
Examples
Attack Rolls
Attack Rolls are a little weird, because you no longer simply care about passing the check; you also care what the natural number was because of Critical Hits and Misses.
Most of the math still checks out: if all you care about is hitting/missing, then the table above can be used, since the scenarios where a Natural 2 hits and a Natural 19 misses are pretty rare in 5e. If, however, you instead care more about the Crits/Auto-Misses, then you should introduce a "subjectivity factor", which you can define however you like: is it important to you that you get a critical hit (or avoid a critical miss)? Then always go Advantage. If not, then use the table above. I generally stick to the table personally, but "clutch factor" is one of those hazy things that can't be objectively defined, so you'll need to make that call for yourself.