The first few leaves on my cucumbers are browning too but I don't think that is anything to worry about. If the whole
plant starts to brown then you're probably in big trouble. My watermelons are taking their sweet-ever-loving time getting going. I planted them the beginning of April and am still waiting for fruit. In fact they just started to bloom on Sun or Mon. My watermelons are usually slow to start but once they get going you'd better watch out! And my peas are not doing very well at all but I think that they don't like heat and it is hot here. Probably would help if they didn't get around 12 hours of sun. The worse part of gardening: trying to be patient. :p Anyway, hope this helps put your mind at ease with a few of your difficulties.
Sarah