What are the limits on transferring objects during fireplace-to-fireplace conversations? Is it exploitable?

Early on in chapter 11 of Goblet of Fire, there is a conversation between the Weasley parents and Mr. Diggory. Mr. Diggory’s head is appearing in their fire and he is using this to talk. During this exchange, we get this line:

Mrs. Weasley took a piece of buttered toast from a stack on the kitchen table,
put it into the fire tongs, and transferred it into Mr. Diggory’s mouth.

This shows that objects can be transferred during fireplace-to-fireplace conversations. Are there any limits that are established for this?

What’s made me concerned about this is the fireplace-to-fireplace conversation between Harry and Sirius near the end of chapter 14 of Order of the Phoenix. As Harry was in the Gryffindor common room during this, it’s opened up two uncomfortable questions that I’m hoping will be addressed by the limitations:

• How can Harry and Sirius be struggling to communicate via letter if all that they need to do is appear in the fireplace for a moment and throw a letter in? Surveillance isn’t a major issue; You only need a moment to catch a letter and therefore you can safely do this in the early morning. Furthermore, Harry’s hypothetical reply – throwing a letter in to a fire – is not very suspicious.
• How can Harry consider the Gryffindor common room safe? It has a fireplace that seemingly anyone can send objects through. The vulnerabilities are blatant and really should’ve been mentioned to the boy who has had hidden murderers supposedly trying to kill him for two or three years in a row (Sirius in third year and a then-unknown person in fourth).

Admittedly, after the scene at the end of chapter 17, where Professor Umbridge’s ringed hand appears to try to grab Sirius’ hair through the fire, I’m not filled with optimism.