In Hindi, सलाद is usually an uncountable /material noun. So stick with जूलिया को सलाद चाहिए। IMHO :) Furthermore, there are no articles in Hindi, so एक सलाद would not sound natural even if it were a countable noun.
As for English, "I want a salad" may be added as an acceptable translation.
"I want salad" would only be used in English if, say, one was at a dinner table and there was a bowl of salad. "I want a salad" (a salad entree) is much more commonly used. I believe the Hindi phrase in the question would apply to both of these scenarios, but I'm curious what the mods think.
राज को ठंडा पानी चाहिए (Raj wants cold water) is correct.
You are probably talking about the sentence मुझे ठंडा पानी पसंद है (I want cold water) in a previous lesson. मुझे is essentially मैं + को.
To elaborate, postpositions like को are only used with nouns. For pronouns, we change their form instead. For example, the forms of मैं corresponding to the postpositions को, में, से, के are मुझे, मुझमें, मुझसे, मेरे and so on.