No, not at all -- networking is a big subject and there are a lot of things to learn.
(1) the router is an access point plus a DHCP service which makes it a router, so just turn off the DHCP and it basically is an AP. The old router has all the features you need, you just need to turn off DHCP so you don't have multiple devices trying to assign IP addresses on your single network. And you need to set the specific stuff I mentioned so that the AP works well within your network.
(2) yes, it needs to be an LAN to LAN port connection for what you are doing. If for some reason you needed a second wireless network (i.e. different IP range like the main one was 192.168.0.1, and the second network was 192.168.5.1 and you did not want communication between the networks) you would go LAN to WAN, but that is not what you want here.
(3) You should always look up and read about stuff so you understand it, but basically as an example your gateway router will be 192.168.1.1 (the third number --or octet-- can be from 0 to 254 and each represents a different network -- some brands have a default of 192.168.1.1, some 192.168.0.1, etc., and the last number is the range of devices in that network .1 is the gateway, .255 is the broadcast address and you can use everything in between as part of that /24 network), so you can make your AP 192.168.1.2 and then allow your DHCP to assign 192.168.1.3 to .254, unless you have a printer or other peripheral that works better on a static address. In that case allow the DHCP to assign up to say .200 and assign static address to the devices from .201 to .254. The main thing is to insure that each device gets a different address in the network and that nothing gets the address of the gateway or AP except that particular device.
(4) there is a section in the configuration pages that allows you to change the radio channels. With G wireless there are 11 channels in the US, but only three do not overlap -- 1, 6 and 11 -- see
http://en.wikipedia.org/wiki/IEEE_802.11g-2003#Channels_and_Frequencies
There is a neat little free program called inSSIDer that you can put on one of your laptops to see all of the wireless signals available with information on each including strength and channel.
The connecting wireless device will either select the strongest signal or let you decide, it will not change between them unless you walk to different area of the house and then many consumer grade devices try to hang on to the original signal until they can't any longer, but you won't have an issue of them bouncing between radio sources.