The plants in the bottom photo are weeds, not raspberries, so you can pull them all out. Any canes which are definitely dead i.e. dry and snappable can be cut to the base. You can leave any live canes to fruit this year. Wait and see, or ask granny, if these are summer or autumn fruiting and then Google the appropriate pruning regime.

Follow floral advise, just leave the canes with the green shoots and see if they'll fruit this summer.

If the old central patch has died out and does not produce new sprouts, best to dig it up and allow the perimeter plants to spread back in to the old area.

You should cut all those dead canes back down to the ground. They will pop up new shoots. They're like black berries and mint plants. I had some raspberry plants I planted and didn't want them so I pulled them out and removed as much of the roots I can. Until today i still see little shoots popping out. I can be wrong because I'm looking at the photos on my phone, but those on the bottom looks like new shoots rather than weeds. You can tell if they're raspberry shoots by the stems of the cane if they're fuzzy kind of like spikes

No, those green plants are most definitely not raspberries. They look to me like something in the Lamiaceae like Betony or white dead nettle. I actually don't think the plants with the dead canes are alive since there should be new growth aplenty by this time of year. However there is no harm in waiting a bit longer to be sure.

The dilemma with the raspberry bed pictured is that that vast majority of canes appear to have no life. You want to remove old canes that produced fruit last season (assuming these are floricane variety which it appears they are). You also want to thin plants with life to no closer than 6" but if you can't locate enough canes with live growth then you may be best to dig up and replant the ones with life. While doing the replanting examine the roots for signs of disease. Raspberries have many root diseases and if you have sick roots you may be better to destroy the bed and start new elsewhere.

I agree with Floral that the third picture looks like weeds.

Id cut them to the ground and till the whole area, whatever is in the soil should still grow. Mix in some manure while you are at it and maybe some sand and peat moss if the soil is very compacted.