In response to your first question: Yes, the summary variables for care seeking are reliable, the only question is whether these summary indicators summarize the information in exactly the way you wish to summarize it. You could also create your own summary variables, specifying exactly which sources of care you wish to include. For example, you could use something like the code below, to identify children for whom care was sought from any source (this is just an example that will match the summary variable h32y):

**Generate a variable to identify children for who treatment was sought from ANY source for fever  
g trtany=0
                foreach x in a b c d e f g h i j k l m n o p q r s t u v x {
                                replace trtany=1 if h32`x'==1
                }
replace trtany=0 if h22==1 & trtany !=1

*Prepare a weight variable
gen wgt=v005/1000000

* Tabulate the weighted percentage of children with fever who received any treatment
tab trtany if h22==1 [iw=wgt] 

In response to your second question: If you wish to look at care seeking for symptoms of ARI, you will want to restrict your analysis of care seeking to the children with reported symptoms of ARI. I recommend that you first generate a variable to identify children with symptoms of ARI (see sample code below), and then, when you tabulate the variable h32y, restrict the tabulation to those children. [Note that we recommend defining "symptoms of ARI" as children with a reported cough with rapid/difficult breathing for whom the difficult breathing is related to a problem in the chest, or to a problem in the chest and to a blocked/runny nose, as in the sample code below.]

Example code:

*Generate a variable to identify children with symptoms of ARI
gen ari=1 if  h31c==1 | h31c==3 
* Tabulate the weighted percentage of children with symptoms of ARI who received any treatment
ta h32y if ari==1 [iw=wgt]

In response to your third question: Since female respondents are only asked questions about their children's recent illness for living children under age five, your analysis is already restricted to living children. It should not make any difference whether you drop the dead children from the recode file, because your tabulations should be restricted to living children with recent illness anyways.

I hope this is helpful!