Bad luck or working as intended

So, I haven’t played hearthstone in many years, thought I’d try it again.

Literally every round the AI puts out a card, and every other round I put out one, and every other round ‘I am out of mana’, and the AI has cleared the board of my one minion.

is this normal till you buy… er i mean get better cards?

edit: and is it normal to have to skip your first round every time because all of ilidans 1 mana spells require the enemy to already have minions on the board?

There are exceptions, but most decks (and definitely when playing versus the innkeeper, as you apparently are doing) are about board control. One player tries to get a presence on the board. The other tries to prevent that, and get their own board presence.
So yes, this back and forth of playing and removing minions is to be expected.

When playing versus the innkeeper, you can win with just the cards from the basic set. A great practice tool for new players. (Note that when you start playing against other humans, you’ll quickly discover that they are better than the innkeeper).

Spells that require a target cannot be cast when there is no valid target. That goes for removal spells, but also for buff spells. There also exist spells that can always be cast.
When playing Illidan (the Demon Hunter class) you never have to pass turn 1 because you have a hero power that costs 1 mana. All other classes have a 2 mana hero power and skipping turn 1 is very common for those classes.