What are the factors that drive openness in developed vs developing countries My questions are:


What are the factors (both positive and negative) that drive openness in a country? 
Do they differ between developed (e.g USA) and developing (e.g China) countries? 
Will these factors remain a key factor to drive openness for the respective country in the future?


So far I researched on stage of development, specialisation of each country's skills, degree of trade liberalisation and the geographical size.
I assume you mean openness to international trade, and that you're interested in both policy choices (does the country want to be open) and physical constraints (can they be open).  The main factors that come to mind are:


Size: the smaller you are, the more you are forced to rely on international trade, as it simply isn't feasible to complete many economic operations entirely within your borders.  Lichtenstein and Andorra are much more open than the US or Russia primarily for this reason.
Remoteness and transport costs: if you're tiny, but in the middle of nowhere, like Tuvalu, the cost of trading internationally means that anything you can feasibly produce domestically will be cheaper than imported goods.  There is little point in trying to protect your domestic market because transport costs already provide more protection than you're likely to want.  This also applies to a lot of small landlocked countries, like Burundi.  Some dependencies of more advanced countries overcome this by massively subsidising transport, often linked to military bases.  E.g. consider the money the UK has spent on an airport in St Helena.
Taxation capacity: this matters very little to rich countries, but developing countries often have a small tax base, large informal sector, and find it hard to replace tariffs with alternatives (VAT, income tax, etc).  Some would like to encourage international trade, but are constrained in how quickly they can remove tariffs.
Proximity to the technological frontier: Ha Joon Chang would argue that the history of protectionism in countries like the UK and US make this point very clearly.  If you lag behind your competitors, you're more likely to protect industries you want to catch up.  If you're ahead, you are more likely to advocate for free trade, knowing that the more unconstrained international competition is, the more you will gain.
Relatedly, supply capacity is perhaps the equivalent for developing countries far from the technological frontier.  Some countries have very weak technology but so much cheap labour that they ought to be able to compete in global markets for simple manufactured goods, but lack critical elements necessary to develop successful firms in these areas.  These constraints come in many forms, a couple of the most common are poor physical infrastructure and weak financial services.  If you have supply capacity you will be keener to promote international trade.  This is not an issue for rich countries.
Comparative advantage will tell you what your country is likely to produce and export if very open.  As I explained in this answer, you will be more keen to rely on your comparative advantage if it is in an industry that is experiencing rapid improvements in productivity.  If your advantages are all in stagnant industries, you'll be more tempted to use protection and other state intervention to shift your comparative advantage, and then open your markets.  This is a bigger issue for poorer countries.
Political culture: many countries have attitudes to openness that are not entirely or directly driven by economics.  For instance, some would argue that European economic integration in the late 20th Century was primarily an attempt to reduce continental violent conflict.