From Dark and Darker Wiki
Long question is fine, but prepare for an equally long response that starts with a resounding NO to... well, everything. The answer is complicated but starts by understanding how scaling works (a.k.a Attribute Bonus Ratio) which you can read up on here - https://darkanddarker.wiki.spellsandguns.com/Damage_Calculation#Attribute_Bonus_Ratio Assuming you have skimmed the above, let's dive into it using the values and information from this wiki (as of Oct 30th 2023, some of this is probably subject to change or might outright be wrong at minimal fault of my own).
Q1: "If I have plus 10 magic damage will ignite add 15 magic damage to my weapon instead of 5" A1: To start, I assume by '+10 magic damage' you mean the stat found EXCLUSIVELY on staves/books/crystal balls, as this is very different from +additional magic or +true magic which ARE NOT affected by 'Magic Power Bonus' (henceforth referred to as MPB). Since crystal balls and books only get +8 magical damage at UNIQUE rarity, let's use the staff in our examples which gets +10 at EPIC rarity. Ignite has a scaling of 50% for both the initial hit and the dot, meaning your '+10 magical damage' gets halved to +5 and takes your ignite from a baseline of 5 to an 'amped' amount of 10 damage WITH YOUR STAFF WHILE IT IS OUT (because remember the +10 magical damage is on the STAFF, not your crystal ball and dagger, not your crossbow, and certainly not your ranger's bow/spear). This 10 'amped' damage will be further scaled by 50% (yes, it double dips scaling) of the target's MPB (let's just assume your MPB of 30%). Now we can use this formula I butchered for my examples to figure out the overall damage after "SPD(1+(MPB(SCL)))+AMD(SCL)" (SPD='amped' spell damage which includes any scaled +magical damage for example 5 baseline from ignite and +5 from staff (+10 magical damage scaled by 50%) is 10, SCL=scaling in this case ignite has 50%, AMD=additional magic damage which we will assume is 0) = 10(1+(.30(.5)))+0 = 11.5 initial damage (this initial hit damage can headshot BTW).
Side Note: If you are wondering the burn damage we can plug in the formula again (ignite ticks for 1 damage with 50% scaling) "SPD(1+MPB(SCL)))+AMD(SCL)" = 6(1+(.30(.5)))+0 = 6.9 (nice) TOTAL burn damage assuming an exact 1 second duration (ignoring swing times causing overlapping debuffs etc.)
Bonus Side Note: +true magical damage would be calculated the same way as +additional magic damage except it ignores enemy magic resistance values, therefore it is disingenuous to apply it at the same step that +AMD is applied. Remember, neither of these stats are affected by Magical Power Bonus (MPB).
Q2: "...and will it add the damage to each magic missile" A2: Not anymore, ignite is exclusive to melee/ranged weapon hits (and fists) and you can easily test this on dummies in the starting lobby.