Does the Nikon D3100 DSLR have manual focus and will it work with a F-601 lens?

Does the Nikon D3100 DSLR have manual focus in photo mode and in video mode?

Also, I have an old Nikon F-601 (film) Series E 36~72mm lens - will it work on the D3100?

Yes it has manual focus. That lens will work but it will not autofocus. The light meter will also be unable to handle it so you would be limited to M (manual) mode only. If you feel you must use this lens a D200 is the most affordable option but that does no video.

Alternatively, forget about the old lens and get the 18-105 or 18-55 lens

Manual Focus is a function of the lens though there will be a switch on the body to turn off Auto focus when you want to use Manual with an AF lens

the D3100 and all Nikon Bodies will mount an Nikon F mount lens though some bodies can be damaged by some lenses

all Nikon DSLRs will mount safely any AI or later Nikon lens
any nikon lens with a solid Aperture ring edge all the way around is Pre AI and should not be Mounted

an AI lens will have a skirt part way around the aperture ring. The ridge on this skirt is to tell the camera equipped with AI meter coupling what the aperture setting is. There will also be a post a little further along to tell the camera when the Aperture is set to Minimum so the full aperture range of the lens is available If the skirt is solid all the way around it can damage the Minimum aperture switch on the camera preventing you from using anything but G type lenses.

Series E lenses are pretty good, relatively inexpensive, and are AI or AI-S compatible

AI-S lenses have a small groove machined into the back end of the lens next to the Notch that locks the Lens to the camera body

AI-S example

you can just see the AI-S groove on the rim in front of the Lock Notch

AI example http://www.photosynthesis.co.nz/nikon/ai3528n.html

note the Metering ridge and Minimum aperture Post or Speed post on both aperture rings as well as the holes in the metering prongs

Pre AI example

note the solid Skirt around the aperture ring and the solid metering prongs

while you can use AI lenses they will not allow you to meter with your camera.
you will have to use Manual exposure mode and guess at exposure or use a handheld exposure meter to determine exposure settings

then use the Highlights and Histogram screens on the LCD to determine whether or not exposure is good or you should adjust settings and shoot again

Yes absolutely. Just make sure to use manual mode as it is a non cpu lens…