بسم الله الرحمن الرحيم
الجواب حامداومصليا
For your first part of the question, Please see this, Detailed Ruling on Feminine discharge:
www.muftisays.com/qa/salaah-wudhu/4362-wudhu-and-normal-d...
You don’t need to insert your finger to check just leave a cloth or pad in your underwear then you can determine if your Wudhu has broken or not. However, If you insert your finger in the inner part of the vagina and taking it out, the najasat (impurity) has exited so your Wudhu will be nullified. If your finger didn’t enter the inner part of the vagina then Wudhu is intact.
If you experience continuous discharge for one whole period of Salah time and to the extent that you could not perform Salah then you will be classified as a Ma'zur (excused person). So when Salah time starts you will pray that Salah and other Salah like Nawafil, until the next Salah time which then you will have to renew your Wudhu.
(احسن افتاوی،١/٦١)
صاحب عذر من به سلسل بول أواستطلاق بطن أوانفلات ريح أواستحاضة.........ان استوعب عذره تمام وقت صلاة مفروضة ولوحكما.......وحكمه الوضوء لكل فرض ثم يصلي به فيه فرضاونفلافاذاخرج الوقت بطل
وحكمه الوضوء لاغسل ثوبه ونحو لكل فرض
(الدرالمختارمع ردالمحتار 1\305,281, احكام المعذور,سعيد)
And Allah knows best
28 Jumadal Ula Akhar 1442/ 11 February 2021