If I place a stop loss order at my provider. Is this order directly forwarded to the stock exchange? Or does my provider implement this logic. If so, do they have to declare any delays that arise by checking the market price and adjusting the at-market order price? Are der big differences in this delay guarantees?
Does the exchange support Stop orders? Some do, some don't. You can find it in exchange's documentation. If the answer is "no" but your broker offers it, then Stop orders are managed either by your broker (on the "server side") or maybe by your trading platform (on the "client side"). If the exchange supports Stop orders, then still you need to clarify with your broker whether the orders are sent as Stop orders to the exchange or manages on server or clients side.
You priority should be Exchange, then server side, then client side. This is because of the latency of course. When Stop order is triggered at the exchange, it immediately becomes active and being matched (just after the trade that triggered it and maybe after other stop orders with the same trigger price which were sent earlier). But if the order is managed by your broker on the server side, it's very uncertain how many orders will execute before your "synthetic" Stop order reaches the matching engine. If the exchange doesn't support Stops, then you are competing against many others like you, but if it does, then until your order arrives there may be an avalanche of stops which trigger each other and move the price far away.
It is important to note the difference between "regular" buy / sell orders and "stop-loss" orders in terms of how they enter the order book.
Regular buy/sell orders enter the order book immediately after you enter them with your broker. The orders then sit in the order-book and wait there until they get "hit". Imagine the price is 100 and you want to buy at 80: your bid order will sit there until the price gets to 80 and then will get executed when an offer hits you. If the price is 100 and you want to sell at 120, same thing: your offer order will sit in the order-book and get executed when 120 gets hit by a bid.
Now when the price is 100 and your stop-loss is 120, it means you are short and want to buy at 120. This means that you are bid 120 when the spot price is 100: that means your order does NOT sit in the order book, because it would be immediately executed. Rather, it sits at the exchange or the broker, and when the price reaches 120, the broker or exchange will only then enter your 120 bid into the order book to get hit asap.
Same with the opposite stop-loss: if the price is 100 and your stop-loss is 80, it means you are 80 offer. The order will only enter the order book and be visible to market makers when the price reaches 80.
The main thing to keep in mind is: regular buy or sell orders are always visible to market makers, from the moment you enter them. Stop-loss orders are normally not visible to market-makers, and only appear in the order book when the price reaches your stop.