No, איפה wouldn't be used in this instance. לאן is only used when showing movement towards somewhere. So, "?לאן הוא רץ" and "?איפה הוא משחק"......."Where is he running?" and "Where is he playing?" The first instance could be thought of as "TO where is he running?" to make it a little more clear. Hope that helps! :)
Just for the record, I thought I would mention that הלך is going somewhere on foot. If you go somewhere in a car or a bus, for example it's נוסע (nosea') (just remember it's to ride) or if you are going somewhere on a bicycle it's רוכב. In fact one guy went to get on the bus. Wanting to make sure it went to Jerusalem, he said אני רוצה ללחת לירושלים. The bus driver responded אז לך (So walk!) slammed the door shut, and drove off. Just remember חלך is go when it's on foot, נוסע is when go means ride, נוהג means to drive by the way, but riding a bike is רוכב . Why רוכב? Well it comes from a root רכב which is biblical texts refers to things that drag themselves across the ground, such as snakes, and other creepy-crawlies, and modernly רכבת means train, by the way. You can see the similarities. Oh, and רכבת תחתית is the subway as it's a train that runs underground.
I also wanted to note that if you want to hear the pronunciation by a sabra (native Israeli) or any other language, simply go to www.forvo.com, copy and paste the word there and for most words you can listen to a recording of that word. You can do the same for a ton of languages by the way. I just hoped this would help some people who are beginning their studies.
Are you sure about the biblical meaning of רכב? Just checked Even Shoshan; the biblical examples it gives pretty much match the modern usage - go on an animal's back (modernly it was extended to bicycle).
In the bible there's of course also the noun רכב /rekhev/ - the metal horse chariots which the arch enemies of the Israelites would have and the Isralites would not... (In modern Hebrew it was borrowed as כלי רכב = "vehicle", and even more modernly the כלי is usually omitted and we just say רכב.)
For a bus you use נוסע, to travel. In fact I knew of one guy that was trying to catch the bus to Jerusalem, but wanted to make sure the bus that stopped for him actually went there. He said אני רוצה ללכת לירושלים to which the bus driver said אז לך!!! (so walk!) slammed the door shut and drove off. For cars and buses it's definitely נוסע (to travel on/by) If I recall it's רוכב for trains and motorcycles (taken from the word to slither like a snake but I would still prefer a sabra (native Israeli) confirm the latter. The word from train came from רוכב by the way, which is רכבת . I love Hebrew and all the permutations you can get from a verb. It's a very descriptive language. Of course that's from a kid that used to color toy scrolls when he (I) was a kid.
Haha, cute. If you wanted to be absolutely proper though, you would say, "...a preposition is a perfectly fine thing with which to end a sentence." A bit wordy for everyday use, but you would never end on a preposition if you were writing a formal research paper or an article for a scientific journal.
As a scientist, I can confirm I have definitely ended sentences with prepositions. Even in formal reaearch papers, sometimes you have to. Sometimes, there are only so many phrases to work with. Of course, it depends on the field you work in. Writing in passive voice doesn't make it easy, but it can be accomplished if one has to!
Yes, prescriptivism run amuck, unfortunately! If we cannot first describe how a language is actually used, then we cannot prescribe how it ought to be used—not without being unwarranted and arbitrary (in doing so). Some of our "grammar rules" have more to do with Latin than English. From my experience, Ancient Hebrew and Koine Greek break many of the same 'rules', as well! They're not alone. Here's a short, pithy article on this particular topic: http://blog.oxforddictionaries.com/2011/11/grammar-myths-prepositions/
Not just Latin. Romance languages too. And English uses relative pronoun phrasing as well. Sometimes people don't use them, depending on the case. At any rate, people don't say "Where are you walking to?" in English. They say "Where are you going?" A literal translation would be "To whence are you walking?", which sounds rather old-timey.