A Few Random Walk Questions

[HP]

Okay, so you've got your standard random walk:

Flip a coin. If heads, move one unit right, if not, one unit left. Start at x=0

The chance you will eventually get to x=1 approaches 1 as the number of additional flips you are willing to take approaches infinity, correct?

And again the chance you will eventually make it to say x=100 (or any other whole number) approaches 1 as the number of flips you are willing to take approaches infinity, correct?

I'm pretty sure the answer is yes and yes so far. How about this though:

You start off at x=1

Flip a coin. If heads, increase value by 10%. If tails, decrease value by 10%. Given you are prepared to flip forever, what are the chances you will make it to x=1.1 or higher? Is it 100% ?

If it is 100%, what if you start at x=1 and use a log-normal distribution (which yields an average change of 0) to figure out where your next step lands you. Will you always make it to a value greater than x=1 eventually ?