are orders and trades always created with ascending id

According to the API documentation, the endpoint

GET /api/v3/allOrders

has the note:

If orderId is set, it will get orders >= that orderId. Otherwise most recent orders are returned.

and the enpoint

GET /api/v3/myTrades

has the note:

If fromId is set, it will get trades >= that fromId. Otherwise most recent trades are returned.

Does this mean, that “orderId” and “tradeId” will be always created in ascending sequence? For example:

order1: orderId = 100
order2: orderId = 101
order3: orderId = 102

trade1 from order1: tradeId = 100
trade2 from order1: tradeId = 101
trade1 from order2: tradeId = 102
trade1 from order3: tradeId = 103

If I want to fetch allOrders beginning from a given orderId, does this mean, that I always get the orders from the order with given orderId till the latest created order? And what does the “Otherwise most recent trades are returned” and “Otherwise most recent orders are returned.” means in numbers? The latest 500 trades or orders?

Does this mean, that “orderId” and “tradeId” will be always created in ascending sequence?

Correct.

If I want to fetch allOrders beginning from a given orderId, does this mean, that I always get the orders from the order with given orderId till the latest created order?

Correct, however keep in mind the order limit is still in effect.

And what does the “Otherwise most recent trades are returned” and “Otherwise most recent orders are returned.” means in numbers? The latest 500 trades or orders?

Correct. Also note that if no limit is set, the default limit will be applied.