hey zee, good to see you getting paid work.
i have 2 guidelines for pricing when it comes to animating. the obvious is length. 1-2 minutes is pretty long, so what you'll want to do is look at your difficulty. the sample video is basic shapes and tweens, so figure you can do about 10 seconds of animation per hour. so you're looking at a combined 10-12 hours for animation time. this alone would put you over $100 estimating you want more than $10/hour.
the next thing you're looking at is timeframe. they want the quote from you ASAP, but what is the window of time they want the animation done? will you have to work in your personal time or on a set weekday schedule.
say you do it all in one day per request, and you request $10/hour. you're looking at $80 for the first 8 hours, then you call it free-lance overtime, and charge $60 for the remaining 4. standard time and a half.
you're also going to be working on sound and post-production so you'll have to add up the time for that as well. whether you use the same pay scale or not for that is up to you.
i'm sure you want more than $10/hour, but you also have to realize that as freelance, $10/hour is closer to $13/hour with tax. make your bid wisely because they think of this as well and don't like a greedy off-site worker.
as for the logo i always do flat fees for things like that. well a flat fee with a limit.
say $50 for 5 seconds. $75 for 10 seconds. $100 for 20 seconds. and so on.
you want the brunt of the charge up front. so you can also say you work for $2/second with a 10 second minimum or the like. this will make it more flexible for both parties to add more content.
ready for the bad part?
the worst thing. you're being payed per hour for your first draft. every revision, color change, mind numbingly tedious alteration becomes pro-bono.
you can put a limit to this prior to taking the job. tell them you will only do 2 drafts. anything they forget to tell you before second draft is finished is SoL on their part.
you can charge for 16 hours and end up putting in 40+ in revising and re-writing because the client isn't clear or doesn't know what they want from the beginning.
best advice i can say is to give them a taste free. make 1-2 seconds of the animation and show them a few things, skill, adaptability, and give them a chance to tell you what they really want.
good luck with this zee, it's an unsatisfying, non gratifying way to work. but if it's what you love, it's what you do.