Rose plants are one of the most difficult plants to maintain, especially when they are grown in pots. The hybrid, grafted, varieties need special care. I was an avid gardener, and when space permitted, I grew a variety of roses, but they never survived for long despite all the feeding and care.
At this juncture, I will not advise you to, change the soil, as the plant will not be able to take the stress of being uprooted. Moreover, this is not the season for re-potting, that is best done when the weather is cooler. Fertilising a plant when it is in distress is also avoidable.
Check to see if your plant is alive. Scrape a tiny piece off the stalk, with your nail or a knife and check if the inside is green. If found to be white that part is dead. Snip it off, but be careful how much you prune, for two reasons, one is the stress bit, the other concerns the grafting. Identify the point where the plant has been grafted. You will be able to tell, by its knobby appearance. Do not prune below that point. Be careful while pruning, use a clean tool and ensure that you do not spread the fungus through the tool. Wipe it clean, before each use.
Your plant seems to be affected by a fungal infection. The spider-web like substance was also due to a pest. In all probability, you brought home a diseased and infected plant. Invest in some gardening equipment to tackle such problems.
An organic fungicide can be sprayed on the plant, you can get these online or at a nursery. Use as per direction. Spray the fungicide after the pruning and repeat as necessary. At this point do not leave the plant under direct sunlight, for long hours. Keep it away from direct sunlight, until it recovers, but keep it outdoors.
Water the plant carefully, too much water could cause root rot. Make sure the soil is moist, at all times. Feed the plant after a few days, when you see it has begun to recover. A slow release fertiliser is best, if not use a liquid one, but dilute it before using. Over fertilisation will also kill the plant.
I suggest you visit the nursery and discuss the issue with the gardener there. He's the one who can help identify the problem and provide a solution. The next time you bring home a plant, speak to the gardener on how to care for it.
“Those who can really do what they promise don't first pause to promise what they can do.” - Bill Willingham