How many days of daily quests it'll take for you to actually complete all the requirements for the molten front offensive and gather enough champion seals to buy all mounts from the argent tournament?
Molten Front -- Up to about 29 days; see this comment for a breakdown. Do note that the the comment is older, but I've found no indication that the number of Marks awarded have been increased since then.
It is apparently possible -- per this guide -- to realm hop and grab the alternate dailies that were not originally offered to you. Doing this would decrease your time to completion, though YMMV depending on what other quests you can find.
Argent Tournament -- There are 14 mounts available:
- Five available for 5 seals each plus gold
- Seven available for 100 seals each
- Two available for 150 seals each
That's 1025 seals needed for all mounts. You can obtain a max of 14/day with dailies, but it's also possible to solo (at max) Trial of the Champion (Heroic) for 3 more seals.
So, with only dailies, you'll need 74 days; include Trial and you'll only need 61. See this comment for a breakdown.