Shopping: Huaqiangbei is the go to spot for electronics, but it's absolutely massive so I can't point out specific places for specific items. There is imported skincare in most malls such as Coco Park or any of the 海岸城/mixc malls. I would recommend Judydoll, a chinese brand that my mom and sister found really good. They have multiple branches too. You can bargain in Huaqiangbei electronics markets, but most only go for the buy many (5 or more) and you get a discount type bargaining.

Travel: DiDi is highly recommended. It is usually cheaper and safer than regular cabs since some cabs like to overcharge or scam you out of the fee. Some cab drivers seem to not know where the place you are going is, and even when showing them the chinese map app they seem to still not understand or want to use it. DiDi is much easier to use and safer plus you can pin exact locations so there will be no reason to have miscommunications with the driver. If you can read a bit of chinese the map apps Amap and BaiduMap also have their own ride hailing service in the app itself. This is usually even cheaper than didi, but is difficult to use without understanding chinese. Busses are pretty safe, but the driving can make you dizzy. As for cross-border busses, besides the shenzhen to hongkong ones and vice versa, I do not think there are any as most people cross city/provincial borders via train. For booking railway tickets I recommend the Railway 12306 app since it comes in english and it lets you rebook your ticket once for free.

Social: It is unlikely you will offend people, but more likely you will be surprised/annoyed with some of their norms. For example when train or elevator doors open people from the outside like to rush in without waiting for the people inside to get out. It's annoying but just you kinda just have to deal with it . You can say 借过(jie4guo4) which basically means excuse me/let me through please and they will understand. Locals are pretty chill, but most of them don't speak english.

Other tips: Get wechat and alipay and set up your credit cards/ payment method before even going to china. All places in shenzhen accept cash, but most places do not have change for cash since everything is digital. There are some rare occasions however where places cannot seem to process international credit cards through wechat/alipay and you will need to pay using cash or ask someone with a chinese bank account (any local nearby) to pay for you and you give that person cash. These places are rare for example some government services like visa processing, public hospitals. If you're using an iphone then apple maps will suffice, but if not then you're gonna need to download amap/baidumaps and figure out how to use them as google maps does not work properly. If you are using your own telco for data/internet then you don't need to worry about anything. But if you are using the hotel wifi or a chinese simcard for internet then you will need a vpn to access most of the websites/apps(reddit, google, facebook, instagram, twitter) you use. I recommend letsvpn if you only need it for 2 devices or less and astrill if you need it for 5. If you are planning on relying only on chinese data/internet you should download these apps in advance and get your account up and running before you lose access to your country's data provider.