I have been cycling now for almost 6 years. I commute from home to work and I carry a laptop along with work clothes probably a sweater, an official shirt, and some bike tools. My estimated distance on a daily basis is 15km. I have experienced some back problems but always thought it was my posture while using the laptop. How long should I continue like this before I start developing real back problems?
This is an impossible question to answer without a physical examination by a medical expert, which I highly recommend. Enduring back pain and poor posture are not things you want to take lightly, as many people in the 'over 50' demographic will attest to. When you ask "how long to continue with this" - I presume you mean put up with back pain - I would say you should do something about it yesterday.
Personally, I think is it very unlikely carrying the backpack, with the weight you describe, is the root cause of your back pain. A healthy back should be able to cope with this kind of load with no ill effect. However, if you have underlying problems, or a poor bike fit, it could aggravate an otherwise hidden problem. Moving the weight to panniers would therefore be a reasonable step for you to take—the advantages of panniers over backpacks when riding make this a worthwhile exercise even if one didn't have back problems.
I would book an appointment to see a professional, but you have several good options—a coin toss between a Bike fit, Osteopath/Chiropractor/Physiotherapist consultation, and a workstation ergonomic assessment. Look for a sports Osteo/Chiro/Physio with an interest in cycling, or a bike fitter with a background in one of these (they are more common than unicorns, but not much...). Start with one and see how far you get. Each of these should be able to refer you to one of the others should it be needed.
The root cause of most people's back pain is lack of core strength; moderate cycling (as many commuters do) is not a great activity for building core strength, so you might want to add off-bike exercises targeting your core, if not already doing them.
Can't really give an answer - health related matters vary too much between individuals.
One consideration is your backpack itself - the common "cloth sack with straps" style is not ideal for cycling because one gets very sweaty, and the load tends to move around creating pressure spots on your back.
Some bags have a padded structure sewn into the back board, and others have a full-on frame made with struts of CF or plastic or even metal. You want a bag that is "just big enough" for your normal loadout and has just enough protection.
A bag designed for comfortable walking may not be good for riding either - on a bike you are tilted much further forward than when walking.
If the bag is cinched up tight behind your head then it tends to help with aerodynamics behind your head/helmet.
But if the bag is too wide it interferes with the airstream more than it helps, and also obstructs your "over-the-shoulder" glances.
For an average-sized laptop, try letting the straps out so the backpack rides a bit lower. This will put the pack lower on your back. Some people find a waist-band or hip-band helps take the weight here, and reduce what's pulling on your shoulders while pressing on your ribs and spine.
Other options include no-backpack and carrying the laptop in a pannier, basket, or on the parcel rack. An oft-overlooked option is simply don't cart the laptop around - I have to do so every day for one week in four, but the other three weeks I leave it at work.
Clothing can be rolled and stored in a jersey pocket. I also make sure to have spare clothes at work, and once showered I'm happy to wear the same shirt for a couple of days. This depends on your job of course.
For overall bike comfort, you might choose to get a bike-fit done, or post a photo of you on your bike, viewed from the side and we may have comments.
If you use laptop heavily at work, your back problems may not be relevant to your cycling. You may just have the screen too low.
Assuming a bearable trail, transporting the laptop in a bag on the pannier rack may be a better choice. It obviously gets more shaking there when you roll over standing on the pedals, but you can control this by reducing speed over bumps. I agree in a few months otherwise you can shake off the heat sink out of CPU for some less ruggedized model of the laptop.
You can also try to move all shock-insensitive items (clothes, bike tools, spare tube - nothing will happen to them) onto the pannier rack, leaving only the laptop on your body.
Most probably it's not the bike, nor your laptop, nor the backpack, not even your back, but your whole body, and what you do with it. If you can cycle 15km you should be able to carry a laptop in your back. But we're a complex toy, and little things can go off balance. :)
Core strength is important, as mattnz says, but I would argue that posture and movement patterns are as important, if not more. So called somatic disciplines that help get "in touch"/better perceive the body and its movement are great to develop those. I like simple exercises like Qi Gong and Feldenkrais; if you want to also gain strength try some yoga; for "quick results" (but less proprioception), Foundation Training is kind of an intense modern yoga to counter modernity, great to strengthen the whole back chain, improve posture and break the hips out of the couch. 20 minutes daily for a month can be a game changer.
A backpack obscures your view over your shoulder, makes it harder to turn to look over your shoulder, and upsets the center of gravity and balance for safe cycling. Put the items in panniers or on a rack - much safer. I say that as someone who has been cycling for sixty years without an accident.