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Does praying at the wrong time count for anything? What does it accomplish? Sources, please.
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Gemara Brachos 26a says that כולי יומא מצלי ואזיל, עד חצות יהבי ליה שכר תפילה בזמנה, מכאן ואילך שכר תפילה יהבי ליה, שכר תפילה בזמנה לא יהבי ליה which means that you still get Sechar Tefila however you lost Sechar Tefila Bezmana.
However the Shulchan Aruch Orach Chaim 108:1 says that once you miss the Zeman better to Daven twice Mincha.
Regarding Davening early it is best not to daven prior to Vasikin. However in times of great difficulty you may Daven as early as Misheyakir (Shulchan Oruch Orach Chaim 58:1). You may even start Davening before Misheyakir up to Yistabach and put on Talis and tefilin at Misheyakir.