I've seen this question before and wondered if a good house rule would be to treat the target as helpless. A helpless character is not defending, and in the case of a willing ally, in a similar fashion, they are not defending either. There is no bonus to the attack roll for a ranged attack, but the defender loses any Dexterity bonus to AC and, their Dexterity is treated as 0 (-5 Dexterity penalty to Armor Class). Thus the target AC would be touch AC, minus any Dex or Dodge Bonuses, minus 5.
As far as the other bonuses, I agree with Zachiel, while some are a bit more obvious than others, ultimately discuss with your DM.
Yes, this was tried in D&D 3.5e as a variant rule.
An officially published version of this rule existed in Unearthed Arcana, a 3rd edition D&D manual of variant rules. It can be used essentially unchanged with the 5th edition.
Unearthed Arcana p.133:
Players Roll All The Dice [...] Attacking and Defending
With this variant, PCs make their attacks just like they do in the standard rules. Their opponents, however, do not. Each time an enemy attacks a PC, the character's player rolls a defense check. If that defense check equals or exceeds the attack score of the enemy, the attack misses.
To determine the creature's attack score, add 11 to the creature's standard attack modifier (the number it would use, as either a bonus or a penalty to its attack roll, if it were attacking in any ordinary situation using the standard rules). For instance, an ogre has standard attack modifier of +8 with its greatclub. That means that its attack score is 19.
To make a defense check, roll 1d20 and add any modifiers that normally apply to your Armor Class (armor, size, deflection, and the like). This is effectively the same as rolling a d20, adding your total AC, and then subtracting 10.
- Attack Score 11 + enemy's attack bonus
- Defense Check 1d20 + character's AC modifiers
If a player rolls a natural 1 on a defense check, his character's opponent has scored a threat (just as if it had rolled a natural 20 on its attack roll).
Note that in D&D's core mechanic, a d20 roll that exactly matches its target DC is considered to succeed -- ties go to the person rolling the dice. So letting the defender roll actually gives them an advantage if you convert the numbers naïvely. This is why it's necessary to add 11 rather than 10 to the attack score to preserve the usual odds.
From the rules for Inspiration in the Player's Handbook, p.126:
If you have inspiration, you can expend it when you make an attack roll, saving throw, or ability check.
So you can't use inspiration to give yourself advantage on a defense roll. This matches the usual case, in which you can't use inspiration to give an opponent disadvantage on an attack roll.
Best Answer
5e doesn't have modifier types
Though most modifiers in 3/3.5e were assigned a specific type and would not stack with other modifiers of the same type, 5e does not have this concept of modifier typing. Modifiers in 5e are effectively untyped, and the only rule about stacking is that bonuses provided by the same source do not stack, as explained by the DMG:
So you can't double an AC bonus by casting the same spell on yourself twice, for instance, but if you are affected by two different spells that both give you an AC bonus, they stack together.
However, there is a caveat. Many effects in 5e confer improved AC by allowing the use of an alternative formula to calculate your base AC, rather than modifying your existing AC - most notably, this is now how wearing armour works. However, as described in the PHB and Basic Rules:
Since you must choose one formula to calculate your AC even if effects mean you have a few choices available to you, this is a way of preventing some stacking effects. Mostly it seems effects which would have provided Armour or Natural Armour bonuses in 3.5 now work in this way.
In general in 5e it's harder to get as many bonuses going at once to stack with, because most useful magic items require attunement; typing the bonuses and preventing them from stacking as well would be overkill. This is part of the general simplification of 5e; you might also note (if you haven't already) that 5e has no such thing as a touch or flat-footed AC, where the types of AC bonuses you had were very relevant.