～てみると

[theseus_]

今日は仕事中頭が痛く、... その後少し寝ても治らず、調べてみると(1)片頭痛は身体を温めすぎると(2)頭痛が増すようで、暖房を切って空気の入れ替えをして、コーヒーを飲むと(3)、その後はマシになりました。

Is "と(1)" means "and..." or "and then..." ? Is it something like "～て、... " ？

Is the meaning of と(2) and と(3) same as と(1) ?

PS. What is the subject of the clause "片頭痛は身体を温めすぎると頭痛が増すようで" ?

 

[gengo]

My translation:
I had a headache at work today. Later on I took a nap but it still wouldn't go away, and when I looked into it, it seems that migraine headaches get worse if your body temperature is too high, so I turned off the heater, let in some fresh air, and had a cup of coffee. After that I felt a little better.

All three of the と's have the same basic meaning, that of "upon doing something." You'll notice that I translated (1) as "when," (2) as "if," and (3) with no direct translation at all.

What is the subject of the clause "片頭痛は身体を温めすぎると頭痛が増すようで" ?

片頭痛 is the topic, and 頭痛 is the subject of the verb 増す.