1. The trade routes wheren't closed. That is a persistently repeated myth. The trade routs where always open just plagued by middle men who would be just as willing to tax the Andalusi as anyone else. The real reason to sail across the atlantic was to open up a trade route Europeans would control and be able to tax each other with.
2. Al-Andalus is just as capable of evolving these institutions from what they had. Just because they're Muslim does not mean they are incapable of figuring out how to make a bank or incorporating a business. It may not be the same thing but it will probably be similar. I mean just for starters, there existed ITTL Islamic mercantile institutions which given time could have evolved into a proper capitalist business. In fact I'd say they could have that happen earlier than Europe because they don't have to work in such a roundabout fashion with monks and knightly orders when they already have trusts and the like.
3. Where do you get the idea Al Andalus lacked a seafaring tradition? Sea faring was a pretty big deal in pretty much all of the Islamic Mediterranean states and Al-Andalus wasn't different.
1. The Andalusi will definitely have an easier time trading east and south than Europeans - the trade would be with coreligionists and in some cases with those of the same culture. There were no Islamic attempts to colonise the new world ITTL - and there's nothing magical about Spain's position. Its just easier, less risky, and more profitable to colonise Africa instead from their position. There was never any oceangoing trade from maghrebi Arabs (the indian ocean trade is a different story.
2. Then why didn't they develop ITTL? Even if you dont want to colonise anywhere, incorporation, issue of stock, and an advanced financial system are still incredible ways to increase a societies wealth. It's a lot more complex than Islam forbidding lending at interest, its about cultural institutions for distributing wealth that required very specific impetuses.
For banking, you need large numbers of wealthy Andalusia to have some reason to liquidate their assets in one location and relocate to another. This needs to be ongoing and predictable. There also needs to be a way for middlemen to charge interest on this transaction.
For incorporation you need to develop the idea that an institution can own something independently of its members. In europe this was monasteries, and the legal principle was transferred to businesses later. Its really hard to get this,because its such a pain to rulers in that it makes it harder to steal other peoples property. In europe,the church was strong enough to resist long enough for the idea of incorporation to take hold. Is there a group in andalusi society that wants to own property independent of inheritance laws, that's also powerful enough to resist the emirs?
Stock issue needs oceangoing trade really - though the caravan trade might be risky enough to encourage the development of a similar institution. If it were though, why didn't it develop?
Its possible for them to develop, but you need to have reasons for it. al-Andalus has to be radically different in the way it views wealth, investment and property to every other culture it is in dialogue with.
I already stated that andalusi Jews provide a way for it to develop with minimal pod's, but you still have the problem of why a people preoccupied with southern, eastern and littoral trading suddenly decide to invest (at huge opportunity cost) in oceangoing trade.
3. Was addressed above.
In a TL where Andalusia survives to the 1800s, it seems likely they might be a colonial bit player in the new world, but their focus will be on africa absent a huge POD.