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If you do not have a greenhouse to keep it growing, happily, then you will need to have a grow light that will provide an adequate amount of light for the plant. 200 watts should suffice.

If you opt to put it in a South facing window, it will stay alive and grow just fine. It will never fruit in those low light conditions, though.

https://www.gardeningknowhow.com/edible/fruits/pineapples/care-of-pineapple-plants.htm

If it's just a little garden spider, he won't hurt anything, but you should be able to spot him. I am more worried that it is spider mites, which are so tiny, you can't see them (unless you shake your plant over a white piece of paper; you should see black dots). They do damage to your plant and their webs are visible. Here is more:

https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-treatment.htm

Lucky you! It looks like a pineapple pup growing. Wait till it is about 8 inches then remove it to start another plant.

https://www.gardeningknowhow.com/edible/fruits/pineapples/pineapple-plant-fruiting.htm

Those pups should produce a pineapple so it may be enough time has not passed. It can take 18 to 32 months for them to fruit. Make sure all their cultural needs are being met. Here is more:

https://gardeningsolutions.ifas.ufl.edu/plants/edibles/fruits/pineapples.html

https://www.gardeningknowhow.com/edible/fruits/pineapples/pineapple-plant-fruiting.htm

This will take about 2 years if it is given near perfect conditions. Typically, they won't flower well indoors if at all. You can do some things to give it a better chance. This will need to be placed under grow lights, or placed outside once it is warm enough. You will want to feed it, periodically, with a well balanced fertilizer of your choice. It will want a rich, light soil that remains slightly moist but not wet or dry. It will appreciate tropical conditions to keep it growing up to speed.

This article will help:

https://www.gardeningknowhow.com/special/children/planting-pineapple-tops.htm

This article will give you more information on the perfect growth parameters, which can be harder to achieve, but will reward you with a better harvest:

https://www.gardeningknowhow.com/edible/fruits/pineapples/care-of-pineapple-plants.htm

This does look like infection. Whether it is bacterial or fungal would likely require testing or a microscope. Your local extension service can help you with testing.

https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm

The cause of this is mostly from stress of overwatering which invites the bacteria/fungi into the suffocating root system. If this has been the case, then fungicides and azadirachtan from neem oil can function as an antifungal agent. You will want to keep all dead debris away from the plant. This will prevent further infection, and cut down on what is already infected. If you can't control watering, or the soil is thick, then proactive organic fungicides may help mitigate these symptoms. Earthworms can help aerate the soil.

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/composting/vermicomposting/benefits-of-garden-worms.htm

https://www.gardeningknowhow.com/edible/fruits/pineapples/care-of-pineapple-plants.htm