If by your second question, you mean any fruit, then there are three main factors you want to consider are 1) chilling factor & dormancy, 2) plant size, and 3) annual vs. perennial.
1). Many fruiting plants either have chilling requirements for fruit set or they simply go dormant in Winter. It will be complicated to give these plants their necessary requirements indoors, especially if growing area part of your living space? Of course, you can try moving them outside of course, but timing needs to be right, and for some of them that may be too cold. For indoor fruiting, consider tropical and subtropical fruits. I'm thinking something like Passionfruit (Passiflora spp.) might give you a good yield for the space, if trellised and lit correctly.
2). Smaller plants will be easier to grow indoors. They will take up less space and be easier to properly light. That's mostly why strawberries (Fragaria spp.) would be a better choice than Blackberries and other brambles (Rubus spp.). Though you might want to consider such northern low-growing delicacies as Cloudberry (Rubus chamaemorus)
3). The easy thing about anual crops is that the plants do not have to be maintained through a dormant season. This might make things easier for indoor growing, depending on the set-up. Recall that many annual 'vegetables' are really savory or semi-sweet fruit fruits, including a number of species in the Nightshade Family (Solanaceae): tomatoes (Solanum lycopersicum), peppers (Capsicum annuum), tomatillos (Physalis spp.), eggplant (Solanum melongena), and garden-huckleberries (Solanum spp.). Garden-huckleberries are usually only sweet with added sugar, but some tomato and tomatillo cultivars are quite sweet. Some can also be short-lived perennials in warm climates. The Gourd family (Cucurbitacea) also has many species grown as annuals including cucumbers (Cucumis sativus), melons (Cucumis melo), squash (Cucurbita spp.), Watermelon (Citrullus lanatus) and a number of others. If plant size and space are not an issue, these should also be considered.