Agreed that a router won't speed anything up.
Think of it like, you have a water faucet that puts out 1 gallon per minute. You have a single water hose connected to it.
Now add a splitter so you can connect 15 more water hoses, yet you're still only getting the same 1 gallon per minute from the source.
Also, most routers get a signal from an ethernet cable so unless you can plug your Galaxy tab in with ethernet it's not going to work. There are also some routers that pick up a current wifi signal then repeat it back out for better range but it only extends how far away you can be from your source of internet, it still won't speed up the signal.
IMHO, anything you purchase from the carrier stores, be it ATT, Verizon or what not, will be more expensive than purchasing online or a standard electronics store. My advice is to teach yourself and research rather than have a salesman tell you what you need. Most of the time. Example: 2 separate occasions, BestBuy employees telling me I must buy an HDMI cable from them, an 8' Monster HDMI cable if I want to actually experience 1080p resolution on my new TV, for $90. When in all actuality I can order an 8' HDMI cable online where I get all my other cables for $5.
Or we were on a trip and I had forgotten the Verizon MiFi charger. So I stopped by the Verizon store and they wanted $40 for a Verizon branded wall charger. I left and went to the WalMart next door and bought a USB wall charger for $10 and a microUSB cable for $8, same thing. Still more than you could buy it for online but saved $32 when I needed it.