Inserts, updates, deletes and reads are generally OK from multiple threads, but answer #1 is not correct. You have to be careful with how you create your connections and use them. There are situations where your update calls will fail, even if your database doesn't get corrupted.
The basic answer.
The SqliteOpenHelper object holds on to one database connection. It appears to offer you a read and write connection, but it really doesn't. Call the read-only, and you'll get the write database connection regardless.
So, one helper instance, one db connection. Even if you use it from multiple threads, one connection at a time. The SqliteDatabase object uses java locks to keep access serialized. So, if 100 threads have one db instance, calls to the actual on-disk database are serialized.
So, one helper, one db connection, which is serialized in java code. One thread, 1000 threads, if you use one helper instance shared between them, all of your db access code is serial. And life is good (ish).
However. If you create multiple helper instances, say one per thread, you are in a bad way. Why? Well, its true the sqlite uses file level locking to prevent database corruption, but the java code simply recognizes the low level error, and deals rather harshly with it. Say you call 'insert' on the SqliteDatabase object. You won't even get an exception. You'll get a little logcat error, but otherwise your app will continue on its merry way, but with no actual insert having been done.
So, multiple threads? Use one helper. Period. If you KNOW only one thread will be writing, you MAY be able to use multiple connections, and your reads will be faster, but buyer beware. I haven't tested that much.
Here's a blog post with far more detail and an example app.
http://kagii.squarespace.com/journal/2010/9/10/android-sqlite-locking.html
Gray and I are actually wrapping up an ORM tool, based off of his Ormlite, that works natively with Android database implementations, and follows the safe creation/calling structure I describe in the blog post. That should be out very soon. Take a look.