Does a one stock leveraged ETF behave like margin?

For example a long leveraged etf may actually go down, even though the stocks it tracks go up, because they use complicated financial instruments to achieve leverage.

Typically, such a discrepancy is because of daily rebalancing, not "complicated financial instruments". That is, each day the ETF will go up if the stocks go up, but compounded returns over time will differ depending on the path of prices. (In some cases, there are other discrepancies, even daily, if the ETF is based on something like the VIX or the oil price that is not directly investable but involves futures.)

In my case, however, I am simply looking for a leveraged, long only tesla ETF. Would an ETF like that, behave more like a simple margin account, meaning in follows the price perfectly, or can it also do something unexpected? After all it wouldn't need rebalancing at least.

See this answer for the problems with having a leveraged ETF that doesn't rebalance. Yes, it would behave somewhat like a simple margin account.

Do they just take all client money and invest all of it on max margin, meaning they will get called, if the stock drops 75%? If they get margin called, do the customers get the opportunity to deposit money to save their own investment?

First, it's not exactly "client money". Assets actually flow into an ETF when institutions deliver assets for new ETF shares (creation mechanism), not when investors buy existing ETF shares on the market.

A leveraged ETF will have a policy for liquidation in the event it has large losses approaching bankruptcy. (This may not correspond to the same level as a margin call for retail investors.) If the ETF is liquidated, this will apply to all shareholders. Liquidation is more likely for an ETF that does not rebalance (or rebalances less frequently), because rebalancing acts like a stop-loss.

Someone told me, that if a 10x etf's tracked stock drops 10%, the fund loses 90%, but when the stock gains 10%, the fund only doubles (and is presumably still at -50%). Is that even possible?

The 10x ETF would lose 100%, not 90%. But yes, leverage effectively magnifies losses more than gains when it comes to geometric compounding. This refers to the loss or gain that occurs between rebalancings. If the stock dropped 10% and then rose 10%, without the ETF being rebalanced again in between, then the stock would be down a net 1% and the ETF would be down 10%.