user, I normally do say you need about six weeks to evaluate a product but an acid should be showing some effect a little quicker, however, your use of it wasn't very consistent. As you're not combo-oily it was perhaps not a good match, sample the other one and see how you get on. A topical clay mask 1-2x a week might help it along too.
Water is fine as a morning rinse if you're normal/dry and don't load up with heavy products the night before but I would urge you to try and keep your face as far away from shower water as possible. I know this is practically impossible but the flushing suggests you are sensitive to temperature and shower water tends to be too hot. Alternatively, shower with tepid water when doing the hair bit. I suspect you're also using an SLS shampoo which isn't all that great for skin as it's stripping, no fun if you're dry.
On account of the fine lines and hidden bumps I think you'd benefit from an AHA more, or perhaps and AHA/BHA combo. I also suspect you're a bit dehydrated (fine lines and the mention of tightness, Nivea a heavy occlusive not working for you, etc.), the Lush products don't really tackle any hydration issues, just dryness. I can't really comment on the serum bar as it's just a bit odd to me, never seen a product like it but I can't really call that a serum either.
You don't wear much makeup so a single oil cleanse should see you through fine but I do find double cleansing more beneficial when you suffer from blackheads. C&P and BB CO are similar though as they're both first cleansers (oil based to remove makeup/spf) so a bit redundant to use after each other.
I'd look towards building the following routine:
AM:
Rinse with water or a mild second cleanser like LRP Toleriane Dermo Cleanser
Hydrating Serum (the superdrug Simply Pure Hydrating Serum, or possibly Asian, or The Ordinaries Buffet)
Moisturiser - use up your current one if it works for you and evaluate when it's nearly finished whether to RP. FWIW I don't really rate Lush as proper skincare, it's much more of a sensorial brand.
A separate SPF - the SPF in the Lush moisturiser really isn't cutting it.
PM:
Oil cleanser - if you like Clinique TDO balm go with that, the liquid version will probably be similar to the BB CO and probably a bit more economical in use. The Superdrug Vit E HCC and the Body Shop Chamomile CB are cheaper versions that are generally well liked.
Second (skin) cleanser - If you can find it easily in the UK, Decubal Face Wash might be of interest (it's like a Danish version of a French pharmacy brand, paraben and fragrance free and high in Niacinamide. Their Face Vital Cream is also worth a try). Good for drier and sensitive skin at a low pH (4.5) and I find a low pH foam better than cream cleansers when dealing with blackheads/pores. LRP Toleriane Dermo or similar otherwise.
Acid toning - as mentioned above. No surprise that I like p50 for AHA, the normal version has Salicylic in it too. Nip+Fab are worth looking at if you don't have fragrance issues.
Serum - whatever specific thing you wish to be tackling here.
Moisturiser/Oil
Mandatory disclaimer : slow and steady is the way to go here. Gradually introduce things with spaces of at least two weeks apart. Only with acids can a bit of purging be expected but otherwise an irritation or reaction is just that. Introduce acids slowly, 1-2x a week building up to every (other) day/2-3x a week.