Advice Needed - First Time Sand Filter

Hi all,
I am not a noob to pools, just sand filters... I have had this pool for a few years and got it on sale with all intex stuff(18' Easy Set, chlorine genny, and pump)... This year my pump wouldn't start and I pulled it apart and the magnet at the shaft was rusty and cracked in several pieces... I looked on craigslist and found way more pump and filter than I needed(Hayward s-220t sand filter, Hayward sp1515 Pump{5000~GPH})... Considerable upgrade from my intex system that was rated at 1800 GPH... Sooo... Now, what I got is used and I got a good deal($100 flat for both)... The sand was dirty(but still filtered well), I am putting new sand in... There was a lot of plaque built up(not sure what) on the bottom of the filter, under the sand... There also appears to be some build up inside of the laterals... Is there any way to clean this that a noobie can do? I see how to take it apart but I question if I can put it back together... I am fairly certain that I could but was wondering if anyone has experience with it... Any advice for that and anything else I should know? I have all the basics of sand filters down(thank god for youtube) and everything is ready to go after I add sand and salt/set up the pool... Here are pictures of how it is right now... I plan on putting it back together in a couple hours so time is kind of important...
Thanks for all the help,
Luke Robinette...

P.S.- I have 5 kids under 10(for a few more days at least) and my pool has to be ready for my 9 year old daughters birthday... I am also aware that I can suck my 4 year old through the hose with the vacuum this thing makes(I've been playing with my new toy)...20160528_151641.jpg20160528_151731.jpg20160528_151555.jpg
 
I tried looking it up but in all honesty Hayward had no diagram of the laterals that I could find... Even if it has some build up in the laterals would it hurt the filtration that much or is it even worth bothering with?
Thank you for all the help,
Luke Robinette.
 
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